Update:

sage: S = SymmetricGroup(4)
sage: S1 = S.subgroup(S.gens()[:1])
sage: S2 = S.subgroup(S.gens()[:1])
sage: S1 is S2
False

Since the same is true for subgroups of permutation groups, I wonder if 
this is intended?

The reason I am asking is that I implemented abelian groups and their 
automorphisms with gap

sage.groups.abelian_gps.abelian_group_gap sage.groups.abelian_gps.
abelian_aut


using unique representations for subgroups. I did I miss something?

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