Topics in Finite Groups

✍ Scribed by Terence M. Gagen

• Publisher: Cambridge University Press
• Year: 1976
• Tongue: English
• Leaves: 95
• Series: London Mathematical Society Lecture Note Series 16
• 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

Cover......Page 1
Title......Page 4
Contents......Page 6
Introduction......Page 8
Notations......Page 9
Elementary results......Page 10
1. BAER'S THEOREM......Page 12
2. A THEOREM OF BLACKBURN......Page 14
3. A THEOREM OF BENDER......Page 16
4. THE TRANSITIVITY THEOREM......Page 19
5. THE UNIQUENESS THEOREM......Page 21
6. THE CASE |TT(F(H))| = 1......Page 27
7. THE PROOF OF THE UNIQUENESS THEOREM......Page 29
8. THE BTJRNSIDE p^q q^b-THEOREM, p, q ODD......Page 39
9. MATSUYAMATS PROOF OF THE p^a q^b-THEOREM, p = 2......Page 40
10. A GENERALIZATION OF THE FITTING SUBGROUP......Page 43
11. GROUPS WITH ABELIAN SYLOW 2-SUBGROUPS......Page 47
12. PRELIMINARY LEMMAS......Page 49
13. PROPERTIES OF A*-GROUPS......Page 56
14. PROOF OF THE THEOREM A, PART I......Page 62
15. PROOF OF THEOREM A, PART E......Page 76
APPENDIX: p-CONSTRAINT AND p-STABILITY......Page 89
References......Page 94