diff --git a/Manifest.toml b/Manifest.toml
index 84f504a..253ecfb 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -2,24 +2,24 @@
 
 [[AbstractAlgebra]]
 deps = ["InteractiveUtils", "LinearAlgebra", "Markdown", "Random", "SparseArrays", "Test"]
-git-tree-sha1 = "da0bf98d73f2f34c35d58981fcf139f16749a394"
+git-tree-sha1 = "f9ec1c158c6d20c14d2e05b190c4377705aff8c4"
 uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
-version = "0.7.1"
+version = "0.9.1"
 
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
 [[BenchmarkTools]]
-deps = ["JSON", "Printf", "Statistics"]
-git-tree-sha1 = "90b73db83791c5f83155016dd1cc1f684d4e1361"
+deps = ["JSON", "Logging", "Printf", "Statistics", "UUIDs"]
+git-tree-sha1 = "9e62e66db34540a0c919d72172cc2f642ac71260"
 uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
-version = "0.4.3"
+version = "0.5.0"
 
 [[BinDeps]]
-deps = ["Compat", "Libdl", "SHA", "URIParser"]
-git-tree-sha1 = "12093ca6cdd0ee547c39b1870e0c9c3f154d9ca9"
+deps = ["Libdl", "Pkg", "SHA", "URIParser", "Unicode"]
+git-tree-sha1 = "46cf2c1668ad07aba5a9d331bdeea994a1f13856"
 uuid = "9e28174c-4ba2-5203-b857-d8d62c4213ee"
-version = "0.8.10"
+version = "1.0.1"
 
 [[BinaryProvider]]
 deps = ["Libdl", "SHA"]
@@ -28,16 +28,22 @@ uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
 version = "0.5.8"
 
 [[Blosc]]
-deps = ["BinaryProvider", "CMakeWrapper", "Compat", "Libdl"]
-git-tree-sha1 = "71fb23581e1f0b0ae7be8ccf0ebfb3600e23ca41"
+deps = ["BinaryProvider", "CMakeWrapper", "Libdl"]
+git-tree-sha1 = "9981f1795919b8f770dc064fe733ba09c2e7c7a9"
 uuid = "a74b3585-a348-5f62-a45c-50e91977d574"
-version = "0.5.1"
+version = "0.6.0"
+
+[[Bzip2_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "3663bfffede2ef41358b6fc2e1d8a6d50b3c3904"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.6+2"
 
 [[CMake]]
 deps = ["BinDeps"]
-git-tree-sha1 = "c67a8689dc5444adc5eb2be7d837100340ecba11"
+git-tree-sha1 = "50a8b41d2c562fccd9ab841085fc7d1e2706da82"
 uuid = "631607c0-34d2-5d66-819e-eb0f9aa2061a"
-version = "1.1.2"
+version = "1.2.0"
 
 [[CMakeWrapper]]
 deps = ["BinDeps", "CMake", "Libdl", "Parameters", "Test"]
@@ -46,16 +52,28 @@ uuid = "d5fb7624-851a-54ee-a528-d3f3bac0b4a0"
 version = "0.2.3"
 
 [[CRlibm]]
-deps = ["Libdl", "Test"]
-git-tree-sha1 = "805164abcd31facf3a7e5b7d803a0d16b23329bc"
+deps = ["Libdl"]
+git-tree-sha1 = "9d1c22cff9c04207f336b8e64840d0bd40d86e0e"
 uuid = "96374032-68de-5a5b-8d9e-752f78720389"
-version = "0.7.1"
+version = "0.8.0"
 
 [[Calculus]]
-deps = ["Compat"]
-git-tree-sha1 = "bd8bbd105ba583a42385bd6dc4a20dad8ab3dc11"
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
 uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
-version = "0.5.0"
+version = "0.5.1"
+
+[[CodecBzip2]]
+deps = ["Bzip2_jll", "Libdl", "TranscodingStreams"]
+git-tree-sha1 = "2fee975d68f9a8b22187ae86e33c0829b30cf231"
+uuid = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd"
+version = "0.7.1"
+
+[[CodecZlib]]
+deps = ["TranscodingStreams", "Zlib_jll"]
+git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da"
+uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
+version = "0.7.0"
 
 [[CommonSubexpressions]]
 deps = ["Test"]
@@ -69,11 +87,17 @@ git-tree-sha1 = "ed2c4abadf84c53d9e58510b5fc48912c2336fbb"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
 version = "2.2.0"
 
+[[CompilerSupportLibraries_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "7c4f882c41faa72118841185afc58a2eb00ef612"
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+version = "0.3.3+0"
+
 [[DataStructures]]
 deps = ["InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "1fe8fad5fc84686dcbc674aa255bc867a64f8132"
+git-tree-sha1 = "4dead20a1606a60292529023d6eac18a1ef6432e"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.17.5"
+version = "0.17.12"
 
 [[Dates]]
 deps = ["Printf"]
@@ -84,25 +108,25 @@ deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
 [[DiffResults]]
-deps = ["Compat", "StaticArrays"]
-git-tree-sha1 = "34a4a1e8be7bc99bc9c611b895b5baf37a80584c"
+deps = ["StaticArrays"]
+git-tree-sha1 = "da24935df8e0c6cf28de340b958f6aac88eaa0cc"
 uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
-version = "0.0.4"
+version = "1.0.2"
 
 [[DiffRules]]
 deps = ["NaNMath", "Random", "SpecialFunctions"]
-git-tree-sha1 = "f734b5f6bc9c909027ef99f6d91d5d9e4b111eed"
+git-tree-sha1 = "eb0c34204c8410888844ada5359ac8b96292cfd1"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "0.1.0"
+version = "1.0.1"
 
 [[Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[ErrorfreeArithmetic]]
-git-tree-sha1 = "a2b7d5a7962e5bfaab0e2e87c9cde7d3087f4e2c"
+git-tree-sha1 = "a5198ab6c8a724dd3965b31ddd11ccde65300f5b"
 uuid = "90fa49ef-747e-5e6f-a989-263ba693cf1a"
-version = "0.4.0"
+version = "0.5.0"
 
 [[FastRounding]]
 deps = ["ErrorfreeArithmetic", "Test"]
@@ -112,53 +136,71 @@ version = "0.2.0"
 
 [[FileIO]]
 deps = ["Pkg"]
-git-tree-sha1 = "351f001a78aa1b7ad2696e386e110b5abd071c71"
+git-tree-sha1 = "3d7cb2c4c850439f19c4d6d3fbe1dce6481cddb1"
 uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
-version = "1.0.7"
+version = "1.2.4"
 
 [[ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "NaNMath", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "4407e7b76999eca2646abdb68203bd4302476168"
+git-tree-sha1 = "869540e4367122fbffaace383a5bdc34d6e5e5ac"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.6"
+version = "0.10.10"
 
 [[GroupRings]]
-deps = ["AbstractAlgebra", "LinearAlgebra", "Markdown", "SparseArrays"]
-git-tree-sha1 = "8a9541783cff6911e35840770d0f004c0d2a13dd"
+deps = ["AbstractAlgebra", "LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "0fb8bccca3155b26231347498bd4949fd49b65b3"
 repo-rev = "master"
 repo-url = "https://github.com/kalmarek/GroupRings.jl"
 uuid = "0befed6a-bd73-11e8-1e41-a1190947c2f5"
-version = "0.3.0"
+version = "0.3.1"
 
 [[Groups]]
 deps = ["AbstractAlgebra", "LinearAlgebra", "Markdown"]
-git-tree-sha1 = "2487fd5e6106dabcafb835b694df08b4d22dde0e"
+git-tree-sha1 = "452c4abb02b4fc5237aca1eaa76c776dd56b2853"
 repo-rev = "master"
 repo-url = "https://github.com/kalmarek/Groups.jl"
 uuid = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
-version = "0.3.0"
+version = "0.4.0"
 
 [[HDF5]]
-deps = ["BinaryProvider", "Blosc", "CMakeWrapper", "Libdl", "Mmap"]
-git-tree-sha1 = "d3ea5532668bf9bdd5e8d5f16571e0b520cbbb9f"
+deps = ["Blosc", "HDF5_jll", "Libdl", "Mmap", "Random"]
+git-tree-sha1 = "cf80ef0b7333e03d78ab6516b56f31f4f7ffa4ae"
 uuid = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
-version = "0.12.5"
+version = "0.13.1"
+
+[[HDF5_jll]]
+deps = ["Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "85bd2e586a10ae0eab856125bf5245e0d36384a7"
+uuid = "0234f1f7-429e-5d53-9886-15a909be8d59"
+version = "1.10.5+5"
+
+[[HTTP]]
+deps = ["Base64", "Dates", "IniFile", "MbedTLS", "Sockets"]
+git-tree-sha1 = "fe31f4ff144392ad8176f5c7c03cca6ba320271c"
+uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
+version = "0.8.14"
+
+[[IniFile]]
+deps = ["Test"]
+git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
+uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
+version = "0.5.0"
 
 [[InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[IntervalArithmetic]]
-deps = ["CRlibm", "FastRounding", "LinearAlgebra", "Markdown", "RecipesBase", "SetRounding", "StaticArrays"]
-git-tree-sha1 = "f97d8d63c3f849b0f545062de4634bc9f100d8ec"
+deps = ["CRlibm", "FastRounding", "LinearAlgebra", "Markdown", "Random", "RecipesBase", "SetRounding", "StaticArrays"]
+git-tree-sha1 = "b2db6ee367b4eb3ee8b009ede8ca809e4fd23d35"
 uuid = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
-version = "0.16.1"
+version = "0.16.7"
 
 [[JLD]]
-deps = ["Compat", "FileIO", "HDF5", "LegacyStrings", "Profile", "Random"]
-git-tree-sha1 = "95fd5d7f129918a75d0535aaaf5b8e235e6e0b0b"
+deps = ["Compat", "FileIO", "HDF5", "LegacyStrings"]
+git-tree-sha1 = "c8c7a9ca4c17a519961a8ec27e508b07ffc9c1a9"
 uuid = "4138dd39-2aa7-5051-a626-17a0bb65d9c8"
-version = "0.9.1"
+version = "0.9.2"
 
 [[JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
@@ -166,6 +208,12 @@ git-tree-sha1 = "b34d7cef7b337321e97d22242c3c2b91f476748e"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 version = "0.21.0"
 
+[[JSONSchema]]
+deps = ["BinaryProvider", "HTTP", "JSON"]
+git-tree-sha1 = "b0a7f9328967df5213691d318a03cf70ea8c76b1"
+uuid = "7d188eb4-7ad8-530c-ae41-71a32a6d4692"
+version = "0.2.0"
+
 [[JuMP]]
 deps = ["Calculus", "DataStructures", "ForwardDiff", "LinearAlgebra", "MathOptInterface", "NaNMath", "Random", "SparseArrays", "Statistics"]
 git-tree-sha1 = "ba7f96010ed290d77d5c941c32e5df107ca688a4"
@@ -179,6 +227,7 @@ uuid = "1b4a561d-cfcb-5daf-8433-43fcf8b4bea3"
 version = "0.4.1"
 
 [[LibGit2]]
+deps = ["Printf"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
 
 [[Libdl]]
@@ -196,25 +245,42 @@ deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
 [[MathOptInterface]]
-deps = ["BenchmarkTools", "LinearAlgebra", "OrderedCollections", "SparseArrays", "Test", "Unicode"]
-git-tree-sha1 = "78427dcc212e0c0ad9658049bc56a50303ad9737"
+deps = ["BenchmarkTools", "CodecBzip2", "CodecZlib", "JSON", "JSONSchema", "LinearAlgebra", "MutableArithmetics", "OrderedCollections", "SparseArrays", "Test", "Unicode"]
+git-tree-sha1 = "27f2ef85879b8f1d144266ab44f076ba0dfbd8a1"
 uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
-version = "0.9.7"
+version = "0.9.13"
 
-[[MathProgBase]]
-deps = ["Compat"]
-git-tree-sha1 = "3bf2e534e635df810e5f4b4f1a8b6de9004a0d53"
-uuid = "fdba3010-5040-5b88-9595-932c9decdf73"
-version = "0.7.7"
+[[MbedTLS]]
+deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
+git-tree-sha1 = "426a6978b03a97ceb7ead77775a1da066343ec6e"
+uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
+version = "1.0.2"
+
+[[MbedTLS_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "c83f5a1d038f034ad0549f9ee4d5fac3fb429e33"
+uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
+version = "2.16.0+2"
 
 [[Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
+[[MutableArithmetics]]
+deps = ["LinearAlgebra", "SparseArrays", "Test"]
+git-tree-sha1 = "e1edd618a8f39d16f8595dd622a63b25f759cf8a"
+uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
+version = "0.2.9"
+
 [[NaNMath]]
-deps = ["Compat"]
-git-tree-sha1 = "ce3b85e484a5d4c71dd5316215069311135fa9f2"
+git-tree-sha1 = "928b8ca9b2791081dc71a51c55347c27c618760f"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
-version = "0.3.2"
+version = "0.3.3"
+
+[[OpenSpecFun_jll]]
+deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
+git-tree-sha1 = "d51c416559217d974a1113522d5919235ae67a87"
+uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
+version = "0.5.3+3"
 
 [[OrderedCollections]]
 deps = ["Random", "Serialization", "Test"]
@@ -230,22 +296,18 @@ version = "0.12.0"
 
 [[Parsers]]
 deps = ["Dates", "Test"]
-git-tree-sha1 = "a23968e107c0544aca91bfab6f7dd34de1206a54"
+git-tree-sha1 = "f8f5d2d4b4b07342e5811d2b6428e45524e241df"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "0.3.9"
+version = "1.0.2"
 
 [[Pkg]]
-deps = ["Dates", "LibGit2", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
+deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
 [[Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
-[[Profile]]
-deps = ["Printf"]
-uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
-
 [[REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -255,9 +317,9 @@ deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [[RecipesBase]]
-git-tree-sha1 = "7bdce29bc9b2f5660a6e5e64d64d91ec941f6aa2"
+git-tree-sha1 = "b4ed4a7f988ea2340017916f7c9e5d7560b52cae"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "0.7.0"
+version = "0.8.0"
 
 [[SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
@@ -283,10 +345,10 @@ deps = ["LinearAlgebra", "Random"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [[SpecialFunctions]]
-deps = ["BinDeps", "BinaryProvider", "Libdl"]
-git-tree-sha1 = "3bdd374b6fd78faf0119b8c5d538788dbf910c6e"
+deps = ["OpenSpecFun_jll"]
+git-tree-sha1 = "e19b98acb182567bcb7b75bb5d9eedf3a3b5ec6c"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "0.8.0"
+version = "0.10.0"
 
 [[StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
@@ -302,6 +364,12 @@ uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[[TranscodingStreams]]
+deps = ["Random", "Test"]
+git-tree-sha1 = "7c53c35547de1c5b9d46a4797cf6d8253807108c"
+uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
+version = "0.9.5"
+
 [[URIParser]]
 deps = ["Test", "Unicode"]
 git-tree-sha1 = "6ddf8244220dfda2f17539fa8c9de20d6c575b69"
@@ -314,3 +382,9 @@ uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
 [[Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
+
+[[Zlib_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "2f6c3e15e20e036ee0a0965879b31442b7ec50fa"
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+version = "1.2.11+9"
diff --git a/Project.toml b/Project.toml
index ad71915..d5cb441 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "PropertyT"
 uuid = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d"
 authors = ["Marek Kaluba <kalmar@amu.edu.pl>"]
-version = "0.3.1"
+version = "0.3.2"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
@@ -12,16 +12,16 @@ IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 JLD = "4138dd39-2aa7-5051-a626-17a0bb65d9c8"
 JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
-MathProgBase = "fdba3010-5040-5b88-9595-932c9decdf73"
-Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [compat]
-AbstractAlgebra = "^0.7.0"
-GroupRings = "^0.3.0"
-Groups = "^0.3.0"
-julia = "≥ 1.1.0"
+AbstractAlgebra = "^0.9.0"
+GroupRings = "^0.3.1"
+Groups = "^0.4.0"
+IntervalArithmetic = "^0.16.0"
+JLD = "^0.9.0"
+JuMP = "^0.20.0"
+julia = "^1.3.0, ^1.4.0"
 
 [extras]
 SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"
diff --git a/REQUIRE b/REQUIRE
deleted file mode 100644
index 12f454a..0000000
--- a/REQUIRE
+++ /dev/null
@@ -1,8 +0,0 @@
-julia
-AbstractAlgebra
-Groups
-GroupRings
-IntervalArithmetic
-JuMP
-JLD
-SCS
diff --git a/src/1712.07167.jl b/src/1712.07167.jl
index ac9d707..4eb5d82 100644
--- a/src/1712.07167.jl
+++ b/src/1712.07167.jl
@@ -1,5 +1,3 @@
-using Printf
-
 ###############################################################################
 #
 #  Settings and filenames
diff --git a/src/1812.03456.jl b/src/1812.03456.jl
index bf36e78..ff3a71b 100644
--- a/src/1812.03456.jl
+++ b/src/1812.03456.jl
@@ -2,8 +2,8 @@ indexing(n) = [(i,j) for i in 1:n for j in 1:n if i≠j]
 
 function generating_set(G::AutGroup{N}, n=N) where N
 
-    rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing(n)]
-    lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing(n)]
+    rmuls = [Groups.transvection_R(i,j) for (i,j) in indexing(n)]
+    lmuls = [Groups.transvection_L(i,j) for (i,j) in indexing(n)]
     gen_set = G.([rmuls; lmuls])
 
     return [gen_set; inv.(gen_set)]
diff --git a/src/PropertyT.jl b/src/PropertyT.jl
index f56a3a9..8c405ce 100644
--- a/src/PropertyT.jl
+++ b/src/PropertyT.jl
@@ -4,7 +4,6 @@ module PropertyT
 using AbstractAlgebra
 using LinearAlgebra
 using SparseArrays
-using Markdown
 using Dates
 
 using Groups
@@ -15,8 +14,6 @@ using JuMP
 
 import AbstractAlgebra: Group, NCRing
 
-import MathProgBase.SolverInterface.AbstractMathProgSolver
-
 include("laplacians.jl")
 include("RGprojections.jl")
 include("orbitdata.jl")
diff --git a/src/RGprojections.jl b/src/RGprojections.jl
index ef7f94d..50ceb86 100644
--- a/src/RGprojections.jl
+++ b/src/RGprojections.jl
@@ -3,7 +3,6 @@ module Projections
 using AbstractAlgebra
 using Groups
 using GroupRings
-using Markdown
 
 export PermCharacter, DirectProdCharacter, rankOne_projections
 
@@ -55,7 +54,7 @@ for T in [PermCharacter, DirectProdCharacter]
     end
 end
 
-characters(G::Generic.PermGroup) = (PermCharacter(p) for p in AllParts(G.n))
+characters(G::Generic.SymmetricGroup) = (PermCharacter(p) for p in AllParts(G.n))
 
 function characters(G::DirectPowerGroup{N}) where N
     nfold_chars = Iterators.repeated(characters(G.group), N)
@@ -80,7 +79,7 @@ function central_projection(RG::GroupRing, chi::AbstractCharacter, T::Type=Ratio
     return result
 end
 
-function alternating_emb(RG::GroupRing{Gr,T}, V::Vector{T}, S::Type=Rational{Int}) where {Gr<:Generic.PermGroup, T<:GroupElem}
+function alternating_emb(RG::GroupRing{Gr,T}, V::Vector{T}, S::Type=Rational{Int}) where {Gr<:AbstractAlgebra.AbstractPermutationGroup, T<:GroupElem}
     res = RG(S)
     for g in V
         res[g] += sign(g)
@@ -88,7 +87,7 @@ function alternating_emb(RG::GroupRing{Gr,T}, V::Vector{T}, S::Type=Rational{Int
     return res
 end
 
-function idempotents(RG::GroupRing{Generic.PermGroup{S}}, T::Type=Rational{Int}) where S<:Integer
+function idempotents(RG::GroupRing{Generic.SymmetricGroup{S}}, T::Type=Rational{Int}) where S<:Integer
     if RG.group.n == 1
         return GroupRingElem{T}[one(RG,T)]
     elseif RG.group.n == 2
@@ -142,7 +141,7 @@ function rankOne_projection(chi::PermCharacter, idems::Vector{T}) where {T<:Grou
     throw("Couldn't find rank-one projection for $chi")
 end
 
-function rankOne_projections(RG::GroupRing{G}, T::Type=Rational{Int}) where G<:Generic.PermGroup
+function rankOne_projections(RG::GroupRing{<:Generic.SymmetricGroup}, T::Type=Rational{Int})
     if RG.group.n == 1
         return [GroupRingElem([one(T)], RG)]
     end
@@ -170,7 +169,7 @@ function rankOne_projections(RBn::GroupRing{G}, T::Type=Rational{Int}) where {G<
     N = Bn.P.n
     # projections as elements of the group rings RSₙ
     Sn_rankOnePr = [rankOne_projections(
-            GroupRing(PermGroup(i), collect(PermGroup(i))))
+            GroupRing(SymmetricGroup(i), collect(SymmetricGroup(i))))
         for i in typeof(N)(1):N]
 
     # embedding into group ring of BN
@@ -208,15 +207,16 @@ end
 #
 ##############################################################################
 
-@doc doc"""
-    products(X::Vector{GroupElem}, Y::Vector{GroupElem}, op=*)
-> Returns a vector of all possible products (or `op(x,y)`), where $x\in X$ and
-> $y\in Y$ are group elements. You may specify which operation is used when
-> forming 'products' by adding `op` (which is `*` by default).
+"""
+    products(X::Vector{GroupElem}, Y::Vector{GroupElem}[, op=*])
+Return a vector of all possible products (or `op(x,y)`), where `x ∈ X` and
+`y ∈ Y`. You may change which operation is used by specifying `op` argument.
 """
 function products(X::AbstractVector{T}, Y::AbstractVector{T}, op=*) where {T<:GroupElem}
     result = Vector{T}()
     seen = Set{T}()
+    sizehint!(result, length(X)*length(Y))
+    sizehint!(seen, length(X)*length(Y))
     for x in X
         for y in Y
             z = op(x,y)
@@ -229,25 +229,21 @@ function products(X::AbstractVector{T}, Y::AbstractVector{T}, op=*) where {T<:Gr
     return result
 end
 
-@doc doc"""
-    generateGroup(gens::Vector{GroupElem}, r=2, Id=parent(first(gens))(), op=*)
-> Produces all elements of a group generated by elements in `gens` in ball of
-> radius `r` (word-length metric induced by `gens`).
-> If `r(=2)` is specified the procedure will terminate after generating ball
-> of radius `r` in the word-length metric induced by `gens`.
-> The identity element `Id` and binary operation function `op` can be supplied
-> to e.g. take advantage of additive group structure.
 """
-function generateGroup(gens::Vector{T}, r=2, Id::T=one(parent(first(gens))), op=*) where {T<:GroupElem}
+    generateGroup(gens::Vector{GroupElem}, r, [op=*])
+Produce all elements of a group generated by elements in `gens` in ball of
+radius `r` (word-length metric induced by `gens`). The binary operation can
+be optionally specified.
+"""
+function generateGroup(gens::Vector{T}, r, op=*) where {T<:GroupElem}
     n = 0
     R = 1
-    elts = gens
-    gens = [Id; gens]
+    elts = [one(first(gens)); gens]
     while n ≠ length(elts) && R < r
         # @show elts
         R += 1
         n = length(elts)
-        elts = products(elts, gens, op)
+        elts = products(gens, elts, op)
     end
     return elts
 end