Lemmas For Sylow Theory
Channel: Andrew Misseldine
Date: 2022-01-14

In this video, we present and prove two lemmas of group theory that will help us develop the theory of Sylow subgroups. In particular, we prove that if an element of p-power order normalizes a Sylow subgroup then it belongs to that Sylow subgroup, and how to count the number of H-conjugate of a subgroup K, where H is also a subgroup.

This is lecture 7 (part 1/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4230 - Abstract Algebra II at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at: 
https://drive.google.com/file/d/1W5DkDt5ZYotcsZHsDtMR4z6PNaGJztQY/view

This lecture is based upon Section 15.1 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.