Tag Archives: Sylow’s theorem

The Fitting subgroup

I have talked a bit about the Frattini subgroup. Time for its big brother. The definition of the Fitting subgroup F(G) of a finite group G is the unique maximal normal nilpotent subgroup of G. As such, of course, it … Continue reading

Posted in exposition | Tagged , , , | 3 Comments

A crash course on group theory

I have just finished a crash course on group theory at Universidade de Lisboa. The notes are here. From the preface: On a visit to Universidade de Lisboa in November 2016, I was asked to give a “crash course” in … Continue reading

Posted in Lecture notes | Tagged , , , , , , , , , , , , | 1 Comment

Notes on finite groups

As an escape from having too much to do, I have combined and lightly revised the notes from my MSc course on finite groups, and posted them here. I tried to steer a middle course between soluble groups and simple … Continue reading

Posted in exposition | Tagged , , , , , | 2 Comments

The symmetric group, 10

I want to say a few words about the connection of the symmetric group with some of the classic nineteenth-century theorems of group theory, by Lagrange, Cayley and Sylow. Lagrange Lagrange’s Theorem states that the order of a subgroup of … Continue reading

Posted in exposition, history | Tagged , , | 1 Comment