Questions tagged [abelian-groups]
For questions about groups whose elements commute.
253 questions
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abelian p-group not divisible [closed]
why if G is an abelian p-group not divisible then exists an element g in G which is not divisible by p?
thanks
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Every abelian group can be embedded into a ring [closed]
Let $(G,0,+)$ be an abelian group. Does there always exist a ring with unity $(R,0,1,+,\cdot)$ and an injective homomorphism of groups $ \psi:(G,0,+)\rightarrow (R,0,+)$?
Is this hard to prove, or are ...
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Are isomorphic quotients of abelian groups induced by automorphisms? [closed]
If I have an (abelian) group $G$ and an automorphism $\sigma: G \to G$ then for any subgroup $H$ of $G$ there is an induced isomorphism $G/H \cong G/\sigma(H)$ given by the map $gH \mapsto \sigma(g)\...
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