Questions tagged [abelian-groups]
For questions about groups whose elements commute.
254 questions
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Local cross sections in infinite dimensional groups
Let $G$ be an (infinite dimensional) compact connected abelian group and $H$ be a closed subgroup of $G$. The quotient morphism $G\to G/H$ may not possess a local cross section, there are examples ...
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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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Categories with canonical factorizations into products satisfying two particular properties
An old splitting theorem for (Hausdorff) locally compact abelian (LCA) groups says that any LCA group $L$ is isomorphic to a direct product of $\mathbb{R}^n$ and $L_1$, where $L_1$ contains a compact-...
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Does an abelian group acting on a riemaniann manifold define an othogonal foliation?
This question is related to my previous question. Suppose that a group $G$ acts freely and properly on a Riemaniann manifold $(M, g)$. Than the orbits form a foliation for $M$. For $p \in M$, let $V_p$...
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