diff --git a/src/new_types.jl b/src/new_types.jl
index ca34915..5195228 100644
--- a/src/new_types.jl
+++ b/src/new_types.jl
@@ -131,7 +131,16 @@ end
 
 function FreeGroup(A::Alphabet)
     @boundscheck @assert all(KnuthBendix.hasinverse(l, A) for l in KnuthBendix.letters(A))
-    return FreeGroup(KnuthBendix.letters(A), A)
+    ltrs = KnuthBendix.letters(A)
+    gens = Vector{eltype(ltrs)}()
+    invs = Vector{eltype(ltrs)}()
+    for l in ltrs
+        l ∈ invs && continue
+        push!(gens, l)
+        push!(invs, inv(A, l))
+    end
+
+    return FreeGroup(gens, A)
 end
 
 function FreeGroup(n::Integer)
diff --git a/test/fp_groups.jl b/test/fp_groups.jl
index 19fc9f4..d49a032 100644
--- a/test/fp_groups.jl
+++ b/test/fp_groups.jl
@@ -1,7 +1,11 @@
 @testset "FPGroups" begin
     A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5])
 
+    @test New.FreeGroup(A) isa New.FreeGroup
+    @test sprint(show, New.FreeGroup(A)) == "free group on 3 generators"
+
     F = New.FreeGroup([:a, :b, :c], A)
+    @test sprint(show, F) == "free group on 3 generators"
 
     a,b,c = gens(F)
     @test c*b*a isa New.FPGroupElement