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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, firstorder logic, groups of prime power order, infinite groups, JordanHolder 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, JordanHolder 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 nineteenthcentury 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