UID:
almafu_9960119725402883
Format:
1 online resource (vii, 260 pages) :
,
digital, PDF file(s).
ISBN:
0-511-75941-X
Series Statement:
Cambridge tracts in mathematics ; 124
Content:
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of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place.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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
pt. I. Fischer's Theory. 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 -- pt. II. The existence and uniqueness of the Fischer groups. 7. Some group extensions. 8. Almost 3-transposition groups. 9. Uniqueness systems and coverings of graphs. 10. U[subscript 4](3) as a subgroup of U[subscript 6](2). 11. The existence and uniqueness of the Fischer groups -- pt. 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. Normalizers of subgroups of prime order in Fischer groups.
,
English
Additional Edition:
ISBN 0-521-10102-6
Additional Edition:
ISBN 0-521-57196-0
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9780511759413
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