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# 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 Fitting subgroup, Frattini argument, nilpotence, Sylow's theorem
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 Classification of Finite Simple Groups, finite groups, first-order logic, groups of prime power order, infinite groups, Jordan-Holder Theorem, locally finite groups, oligomorphic permutation groups, periodic groups, profinite groups, residually finite groups, Sylow's theorem, topology
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 composition series, extension theory, group action, Jordan-Holder Theorem, simple groups, Sylow's theorem
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 Cayley's theorem, Lagrange's theorem, Sylow's theorem
1 Comment