@testset "FPGroups" begin
    A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5])

    @test FreeGroup(A) isa FreeGroup
    @test sprint(show, FreeGroup(A)) == "free group on 3 generators"

    F = FreeGroup([:a, :b, :c], A)
    @test sprint(show, F) == "free group on 3 generators"

    a,b,c = gens(F)
    @test c*b*a isa FPGroupElement

    # quotient of F:
    G = FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b])

    @test G isa FPGroup
    @test sprint(show, G) == "⟨ a  b  c | \n\t  a*b => b*a  a*c => c*a  b*c => c*b ⟩"
    @test rand(G) isa FPGroupElement

    f = a*c*b
    @test word(f) isa Word{UInt8}

    aG,bG,cG = gens(G)

    @test aG isa FPGroupElement
    @test_throws AssertionError aG == a
    @test word(aG) == word(a)

    g = aG*cG*bG

    @test_throws AssertionError f == g
    @test word(f) == word(g)
    @test word(g) == [1, 5, 3]
    Groups.normalform!(g)
    @test word(g) == [1, 3, 5]

    let g = aG*cG*bG
        # test that we normalize g before printing
        @test sprint(show, g) == "a*b*c"
    end

    # quotient of G
    H = FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200)

    h = H(word(g))

    @test h isa FPGroupElement
    @test_throws AssertionError h == g
    @test_throws MethodError h*g

    H′ = FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200)
    @test_throws AssertionError one(H) == one(H′)

    Groups.normalform!(h)
    @test h == H([5])

    @test_logs (:warn, "using generic isfiniteorder(::AbstractFPGroupElement): the returned `false` might be wrong") isfiniteorder(h)

    @test_logs (:warn, "using generic isfinite(::AbstractFPGroup): the returned `false` might be wrong") isfinite(H)

    Logging.with_logger(Logging.NullLogger()) do
        @testset "GroupsCore conformance: H" begin
            test_Group_interface(H)
            test_GroupElement_interface(rand(H, 2)...)
        end
    end
end