3-transposition groups
Author(s)
Bibliographic Information
3-transposition groups
（Cambridge tracts in mathematics, 124）
Cambridge University Press, 1997
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- Other Title
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Three-transposition groups
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Hiroshima University Central Library, Interlibrary Loan
: hardback411.63:A-89/HL4010004000409080
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
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of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place.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.
Table of Contents
- 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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