Edited by Peter H. Kropholler
Edited by Graham A. Niblo
Edited by Ralph Stöhr
Publisher: Cambridge University Press
Print Publication Year: 1998
Online Publication Date:April 2010
Online ISBN:9780511666131
Paperback ISBN:9780521635561
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511666131.003
Subjects: Algebra, Geometry and Topology
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Introduction
Whatever one may think of a proof that covers over ten thousand pages of journal articles, some of which have still not appeared in print, the classification of finite simple groups is a remarkable theorem. It says that (apart from the cyclic groups of prime order and the alternating groups) most finite simple groups are groups of Lie type. These are the analogues of the compact Lie groups, defined over a finite field. They admit a uniform description in terms of the fixed points of certain automorphisms related to the Frobenius map, on the corresponding algebraic groups in prime characteristic. The classifying space of a finite group of Lie type fibers over that of the corresponding Lie group with fibers which are cohomologically finite away from the defining characteristic. Apart from the groups of Lie type, there are the alternating groups An (n ≥ 5), and twenty-six other groups called the sporadic simple groups.
The first five sporadic groups were discovered by Mathieu in the late nineteenth century. The remaining twenty-one were discovered in the nineteen sixties and seventies. The largest is the Fischer–Griess Monster, which has order roughly 8 × 1053. For a wealth of information on the sporadic groups and other “small” finite simple groups, the reader is referred to the ATLAS of finite groups [Atlas]. A great deal of effort has gone into trying to understand these sporadic groups.
pp. i-iv
pp. v-vi
pp. vii-viii
List of Participants : Read PDF
pp. ix-xii
On the Cohomology of SL2(ℤ[1/p]) : Read PDF
pp. 1-9
Cohomology of Sporadic Groups, Finite Loop Spaces, and the Dickson Invariants : Read PDF
pp. 10-23
Kernels of Actions on Non-positively Curved Spaces : Read PDF
pp. 24-38
Cyclic Groups Acting on Free Lie Algebras : Read PDF
pp. 39-44
Cohomology, Representations and Quotient Categories of Modules : Read PDF
pp. 45-73
Protrees and Λ-trees : Read PDF
pp. 74-87
Homological Techniques for Strongly Graded Rings: A Survey : Read PDF
pp. 88-107
Buildings are CAT(0) : Read PDF
pp. 108-123
On Subgroups of Coxeter Groups : Read PDF
pp. 124-160
The p-primary Farrell Cohomology of Out(Fp–1) : Read PDF
pp. 161-169
On Tychonoff Groups : Read PDF
pp. 170-187
Word Growth of Coxeter Groups : Read PDF
pp. 188-189
Poly-surface Groups : Read PDF
pp. 190-208
Analytic Versions of the Zero Divisor Conjecture : Read PDF
pp. 209-248
On the Geometric Invariants of Soluble Groups of Finite Prüfer Rank : Read PDF
pp. 249-262
Some Constructions Relating to Hyperbolic Groups : Read PDF
pp. 263-290
Free Actions of Abelian Groups on Groups : Read PDF
pp. 291-295
Finitely Presented Soluble Groups : Read PDF
pp. 296-316