The Classification of the Finite Simple Groups, Issue 3

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American Mathematical Soc., 1998 - Mathematics - 419 pages
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This work offers a single source of basic facts about the structure of the finite simple groups with emphasis on a detailed description of their local subgroup structures, coverings, and automorphisms. The method is by examination of the specific groups, rather than by the development of an abstract theory of simple groups. While the purpose of the book is to provide the background for the proof of the classification of the finite simple groups - dictating the choice of topics - the subject matter is covered in such depth and detail that the book should be of interest to anyone seeking information about the structure of the finite simple groups. The treatment, however, is not self-contained. The authors rely on a small number of standard references whose results they extend and develop. This volume offers a wealth of basic facts and computations. Much of the material is not readily available from any other source. In particular, the book contains the statements and proofs of the fundamental Borel-Tits Theorem and Curtis-Tits Theorem. It also contains complete information about the centralizers of semisimple involutions in groups of Lie type, as well as many other local subgroups.
 

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Contents

I
1
II
2
III
4
IV
5
V
6
VII
7
IX
8
X
13
XXXI
134
XXXII
143
XXXIII
153
XXXIV
170
XXXV
186
XXXVI
204
XXXVII
219
XXXVIII
227

XI
15
XII
16
XIII
17
XIV
22
XV
23
XVI
27
XVII
30
XVIII
31
XIX
36
XX
40
XXI
45
XXII
53
XXIII
63
XXIV
67
XXV
73
XXVI
89
XXVII
91
XXVIII
95
XXIX
106
XXX
119
XXXIX
236
XL
249
XLI
252
XLII
288
XLIII
294
XLIV
302
XLV
311
XLVI
313
XLVII
317
XLVIII
324
XLIX
328
L
335
LI
343
LII
346
LIII
349
LIV
380
LV
383
LVI
385
LVII
399
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About the author (1998)

Ronald Solomon earned his Ph.D. at Yale University. Now teaching at The Ohio State University, Solomon's research area is the theory of finite groups, especially the classification and structure theory of the finite sample groups. Other interests include representation theory of finite groups and finite-dimensional algebras and in the geometries associated with groups. Outside of work, Dr. Solomon's interests include classical music, theater, his children, and the social needs of the underprivileged.