3-Transposition Groups

Contains the first complete published proof of Fischer's Theorem on the classification of 3-transposition groups.

Zusammenfassung
The theory of 3-transposition groups has become an important part of finite simple group theory. This book contains the first complete published proof of Fischer's Theorem on the classification of these groups. Part I is accessible to graduate students in finite groups while Parts II and III are aimed at specialists.

Inhalt
Part I. Fischer's Theorem: 1. Preliminaries; 2. Commuting graphs of groups; 3. The structure of 3-transposition groups; 4. Classical groups generated by 3-transpositions; 5. Fischer's theorem; 6. The geometry of 3-transposition groups; Part II. Existence and Uniquenesss Of The Fischer Groups: 7. Some group extensions; 8. Almost 3-transposition groups; 9. Uniqueness systems and coverings of graphs; 10. U4 (3) as a subgroup of U6 (2); 11. The existence and uniqueness of the Fischer groups; Part III. The Local Structure Of The Fischer Groups: 12. The 2-local structure of the Fischer groups; 13. Elements of order 3 in orthogonal groups over GF(3); 14. Odd locals in Fischer groups; 15. Normalisers of subgroups of prime order in Fischer groups.

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