By
Michael Aschbacher
California Institute of Technology
Cambridge Tracts in Mathematics
(No. 124)
Publisher: Cambridge University Press
Print Publication Year:1996
Online Publication Date:August 2010
Online ISBN:9780511759413
Hardback ISBN:9780521571968
Paperback ISBN:9780521101028
Book DOI: http://dx.doi.org/10.1017/CBO9780511759413
Subjects: Algebra
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of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place.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. Part I of this book 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.
Reviews:
pp. i-iv
pp. v-viii
Part I - Fischer's Theory
pp. 1-5
pp. 6-20
2 - Commuting graphs of groups: Read PDF
pp. 21-29
3 - The structure of 3-transposition groups: Read PDF
pp. 30-38
4 - Classical groups generated by 3-transpositions: Read PDF
pp. 39-57
5 - Fischer's Theorem: Read PDF
pp. 58-90
6 - The geometry of 3-transposition groups: Read PDF
pp. 91-108
Part II - The existence and uniqueness of the Fischer groups
pp. 109-112
7 - Some group extensions: Read PDF
pp. 113-136
8 - Almost 3-transposition groups: Read PDF
pp. 137-146
9 - Uniqueness systems and coverings of graphs: Read PDF
pp. 147-156
10 - U4(3) as a subgroup of U6(2): Read PDF
pp. 157-172
11 - The existence and uniqueness of the Fischer groups: Read PDF
pp. 173-198
Part III - The local structure of the Fischer groups
pp. 199-200
12 - The 2-local structure of the Fischer groups: Read PDF
pp. 201-210
13 - Elements of order 3 in orthogonal groups over GF(3): Read PDF
pp. 211-225
14 - Odd locals in Fischer groups: Read PDF
pp. 226-249
15 - Normalizers of subgroups of prime order in Fischer groups: Read PDF
pp. 250-252
pp. 253-254
pp. 255-256
pp. 257-260