Subgroups of abelian groups:

sage: G.<a, b> = AbelianGroup(2)
sage: A = G.subgroup([a])
sage: B = G.subgroup([b])
sage: A == B
True

Surely not!

On the other hand for vector spaces:

sage: W.<u, v> = QQ^2
sage: U = W.subspace([u])
sage: V = W.subspace([v])
sage: U == V
False

As expected.

-- 
Francis Clarke
Department of Mathematics
University of Wales Swansea
Swansea
SA2 8PP

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