5
votes
2answers
657 views

Geometric interpretation of $BN$-pairs

My question is relative to a geometric interpretation of the $BN$-pairs that arise in Tits' theory of buildings. Here is a definition that comes from an article by G. Stroth (Nonspherical spheres). ...
13
votes
1answer
735 views

A synopsis of Adyan’s solution to the general Burnside problem?

Where can I find a high-level overview of Adyan’s original proof of the existence of finitely generated infinite groups with finite exponent? Additionally: If possible, would an expert ...
19
votes
2answers
1k views

Geometric interpretation of group rings?

For a group $G$, is there an interpretation of $\mathbb C[G]$ as functions over some noncommutative space? If so, what does this space "look like"? What are its properties? How are they related to ...
15
votes
1answer
682 views

Symmetric groups which are not quotients of Z/2Z*Z/3Z

Somehow this question made me think of instances of small exceptions in general, and I remembered the statement I heard once that $S_5,A_6,S_6,A_7,A_8,S_8$ are the only instances of ...
11
votes
5answers
1k views

Abstract nonsense versions of “combinatorial” group theory questions

In particular, I'm just curious whether there's a version of the Sylow theorems (which are very combinatorially-flavored) which allows horizontal and/or vertical categorification? Or at least can be ...