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Questions about the branch of algebra that deals with groups.

3 votes
0 answers
163 views

First reference to the Tits alternative

As we know, the "Tits alternative" is a theorem relating to finitely generated linear groups. I was curious as to where in the literature the Tits alternative is first referred to by this name, as I …
Hollis Williams's user avatar
15 votes
1 answer
457 views

Can a torsion-free group be quasi-isometric to a torsion group?

I have looked around in the literature on group theory and geometric group theory and this looks to be an open question as far as I can tell (by torsion group, I mean as usual a group in which every e …
Hollis Williams's user avatar
2 votes
Accepted

Can a torsion-free group be quasi-isometric to a torsion group?

This is one of many open questions in geometric group theory related to quasi-isometries. Proving things about invariance under quasi-isometries is generically quite tricky, as quasi-isometries do no …
Hollis Williams's user avatar
3 votes

Introductory text on geometric group theory?

For beginners 'A Course on Geometry Group Theory' by Brian Bowditch is nice although quite terse in places, but good for 'setting the scene'.