New page on reading recommendations

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.

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The p-group fixed point theorem

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.

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