Hi there, When I define an abelian group A = AbelianGroup(1,[6]) and then generate a subgroup that actually is the whole group itself, and then compare it to the original group: A.subgroup(list(A.gens())) == A the result may be either True or False. In this example it is False. When defining A as A = AbelianGroup(2,[3,2]) it is False as well, but when I define it as A = AbelianGroup(2,[2,3]) it is True. My guess is that this is because comparison of finite Abelian groups is implemented using their invariant factors, but when you create the group using factors that are not in canonical form or not in increasing order, these are used instead of the ordered list of invariant factors anyway.
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