0:00 Solvability of polynomial equations and solvable Galois groups
1:26 Commutators and commutator subgroups
12:01 Higher commutator subgroups and the lower central series
16:15 Definitions of solvable and nilpotent groups
19:06 Lemmas about solvable and nilpotent groups
22:29 Theorem characterizing nilpotent groups
27:50 Theorem characterizing solvable groups
33:04 The center of a p-group is non-trivial
36:16 Every p-group is nilpotent
38:53 Every group of order p^2 is abelian
In this lecture we discuss properties of solvable and nilpotent groups.
This is a lecture in a graduate course "Groups and Galois Theory".
Here is the complete playlist for this course:
https://www.youtube.com/playlist?list=PLu6jbin1VpDDNAuq_Wa6WGElXYnJQTmOh
