Topics in Finite Groups

✍ Scribed by Gagen T. M., Hitchin N. J. (Ed)

• Year: 2008
• Tongue: English
• Leaves: 93
• Category: Library

✦ Synopsis

These notes derive from a course of lectures delivered at the University of Florida in Gainesville during 1971/2. Dr Gagen presents a simplified treatment of recent work by H. Bender on the classification of non-soluble groups with abelian Sylow 2-subgroups, together with some background material of wide interest. The book is for research students and specialists in group theory and allied subjects such as finite geometries.

✦ Table of Contents

Topics in Finite Groups......Page 1
Contents......Page 4
Introduction......Page 5
Notations......Page 6
Elementary results......Page 7
1. Baer's theorem......Page 9
2. A theorem of Blackburn......Page 11
3. A theorem of Bender......Page 13
4. The transitivity theorem......Page 16
5. The uniqueness theorem......Page 18
6. The case |π(F(H))|=1......Page 24
7. The proof of the uniqueness theorem 5.1......Page 26
8. The Burnside p^a q^b-theorem, p, q odd......Page 36
9. Matsuyama's proof of the p^a q^b-theorem, p=2......Page 37
10. A generalization of the Fitting subgroup......Page 40
11. Groups with abelian Sylow 2-subgroups......Page 44
12. Preliminary lemmas......Page 46
13. Properties of A*-groups......Page 53
14. Proof of the theorem A, part I......Page 59
15. Proof of theorem A, part II......Page 73
Appendix: p-constraint and p-stability......Page 86
References......Page 91