I’ve added a new page of reading recommendations, mostly for undergraduates, to the top. The emphasis is intended to be on well-written and accessible books. Comments and suggestions welcome.

## Archive for July, 2013

## New page on reading recommendations

Posted in Uncategorized on July 31, 2013 | Leave a Comment »

## The p-group fixed point theorem

Posted in math.CO, math.GR, math.NT, tagged finite fields, fixed point theorems, group actions, walks on graphs on July 9, 2013 | 12 Comments »

The goal of this post is to collect a list of applications of the following theorem, which is perhaps the simplest example of a fixed point theorem.

**Theorem:** Let be a finite -group acting on a finite set . Let denote the subset of consisting of those elements fixed by . Then ; in particular, if then has a fixed point.

Although this theorem is an elementary exercise, it has a surprising number of fundamental corollaries.