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Results tagged with geometric-group-theory
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user 22989
Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations
13
votes
Accepted
Can a group be a union of finitely many subgroups of infinite index?
It may well be a lot easier than this, but it follows from the answer to the weaker question Can a group be a finite union of (left) cosets of infinite-index subgroups? that it's not possible.
- 35.2k
6
votes
Accepted
Is the following module over a group ring necessarily infinitely generated?
If $\Gamma$ acts $2$-transitively on an infinite set $X$, then the permutation module $\mathbb{Q}[X]$ will be a counterexample.
For example, take an action of the free group of rank $2$ on a countabl …
- 35.2k
4
votes
Number of orbits for abelian group actions
You could take $G=\mathbb{Z}\times\mathbb{Z}$, $X=G$ with the regular action, and $Y$ the disjoint union of two copies of $X$, and let $\{G_i\}$ be the family of cyclic subgroups of $G$.
- 35.2k