### Can -oids save Group Theory 101?

#### Posted by David Corfield

Can you help Lieven out with some questions?

Posted at February 17, 2009 5:04 PM UTCHave you seen a first-year group theory course starting off with groupoids? Do you know an elegant way to prove a classical group-result using groupoids?

## Re: Can -oids save group-theory 101?

I have seen groupoids introduced early on, perhaps not right at the start. (Where … where else Bangor!)The theorems that work well from a groupoid point of view are the Nielsen Schreier theorem and the Schreier index theorem. These can be found in work by Phil Higgins for instance probably in his reprinted categories and groupoids book (TAC reprints).

I have used groupoids as a tool in courses on group presentation theory. They work well there. Also see Ronnie Brown’s Topology and Groupoids especially chapter 10.