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Results tagged with gr.group-theory
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user 16862
Questions about the branch of algebra that deals with groups.
7
votes
1
answer
377
views
Ascending Chain Condition for finite normalizers
Let $G$ be a group and $H$ a subgroup. Consider the ascending chain of iterated normalizers:
$$
H \trianglelefteq N_G(H) \trianglelefteq N_G(N_G H) \trianglelefteq \cdots \trianglelefteq N^{(k)}_G(H) …
- 687
6
votes
1
answer
918
views
Uniform lattices in semisimple Lie groups
Let $\Gamma$ be a uniform lattice in a semisimple Lie group $G$.
Must $\Gamma$ be virtually torsion-free?
If (1) is true, then does this work more generally if $G$ is reductive?
I am motivated by …
- 687
6
votes
1
answer
432
views
Automorphism groups of virtually cyclic groups
Let $V$ be a virtually cyclic group.
Then is $Aut(V)$ also a virtually cyclic group?
This is true when $V$ is a finite group (zero-ended) and when $V = C_\infty, D_\infty$ (both two-ended).
- 687
3
votes
1
answer
410
views
Baumslag-Solitar subgroups of Poincare duality groups
Can a Poincaré duality group $G$ contain Baumslag--Solitar subgroups $H$ such as BS(1,3) or BS(2,3)?
I don't mean to include those subgroups which are the fundamental group of the torus or Klein bott …
- 687