1,742 reputation
1017
bio website
location
age 30
visits member for 4 years, 2 months
seen 29 mins ago
A nomadic postdoc, currently in Australia.

1d
revised Simple groups and words
added 450 characters in body
1d
answered Simple groups and words
1d
comment Relations between Arboreal Group Theory and Tree Group Actions?
There are too many groups that act faithfully on a rooted binary tree to say very much in complete generality: any group that has a descending chain of subgroups with trivial intersection, such that the subgroups have index powers of $2$, admits such an action. So you need to impose some conditions on either the group (e.g. automata groups) or the action (e.g. branch groups) to obtain a meaningful theory.
Apr
6
comment Lattices in general totally disconnected locally compact groups
Good point Yves, I have edited the answer accordingly. The fact that Neretin's group is compactly generated is also interesting.
Apr
6
revised Lattices in general totally disconnected locally compact groups
added 20 characters in body
Apr
5
revised Lattices in general totally disconnected locally compact groups
added 7 characters in body
Apr
5
accepted Control of $p$-extensions by subgroups of index coprime to $p$
Apr
5
answered Lattices in general totally disconnected locally compact groups
Apr
5
comment Lattices in general totally disconnected locally compact groups
As far as I know, the question of whether a given t.d.l.c. group has lattices is very difficult in general. Willis theory tells you a lot about individual automorphisms, but not so much about the global structure.
Apr
5
revised Control of $p$-extensions by subgroups of index coprime to $p$
edited tags
Apr
5
comment Lattices in general totally disconnected locally compact groups
Given a finitely generated group $\Gamma$ and a Cayley graph $X$ for $\Gamma$, then $\Gamma$ is a uniform lattice in the automorphism group of $X$, which is a (not necessarily discrete) t.d.l.c. group.
Apr
5
asked Control of $p$-extensions by subgroups of index coprime to $p$
Apr
1
awarded  Taxonomist
Apr
1
awarded  Citizen Patrol
Feb
19
revised Uniqueness of composition series for profinite groups
added 259 characters in body
Feb
19
answered Uniqueness of composition series for profinite groups
Feb
17
awarded  Yearling
Oct
26
awarded  Popular Question
Jun
25
awarded  Revival
May
2
comment Extensions with trivial induced outer action
I don't see any reason why $N$ should be abelian unless you impose some additional conditions.