Sporadic Groups is the first step in a programme to provide a
uniform, self-contained treatment of the foundational material on
the sporadic finite simple groups. The classification of the finite
simple groups is one of the premier achievements of modern
mathematics. The classification demonstrates that each finite
simple group is either a finite analogue of a simple Lie group or
one of 26 pathological sporadic groups. Sporadic Groups provides
for the first time a self-contained treatment of the foundations of
the theory of sporadic groups accessible to mathematicians with a
basic background in finite groups such as in the author's text
Finite Group Theory. Introductory material useful for studying the
sporadics, such as a discussion of large extraspecial 2-subgroups
and Tits' coset geometries, opens the book. A construction of the
Mathieu groups as the automorphism groups of Steiner systems
follows. The Golay and Todd modules, and the 2-local geometry for
M24 are discussed. This is followed by the standard construction of
Conway of the Leech lattice and the Conway group. The Monster is
constructed as the automorphism group of the Griess algebra using
some of the best features of the approaches of Griess, Conway, and
Tits, plus a few new wrinkles. Researchers in finite group theory
will find this text invaluable. The subjects treated will interest
combinatorists, number theorists, and conformal field theorists.
General
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