3-Transposition Groups (Cambridge Tracts in Mathematics, Series Number 124)
Cambridge University Press, 3/13/1997
EAN 9780521571968, ISBN10: 0521571960
Hardcover, 272 pages, 23.6 x 16 x 2.5 cm
Language: English
Originally published in English
In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place. Fischer's result, while important and deep (covering a number of complex examples), can be understood by any student with some knowledge of elementary group theory and finite geometry. Thus Part I has minimal prerequisites and could be used as a text for an intermediate level graduate course. Parts II and III are aimed at specialists in finite groups and are a step in the author's program to supply a strong foundation for the theory of sporadic groups.
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.