LEADER 00000nam a2200373 i 4500
001 CR9780511665585
003 UkCbUP
005 20181024165311.0
006 m o d
007 cr nn 008maaau
008 091217s1994 enk s 0 eng d
020 9780511665585|q(electronic bk.)
020 9780521420495|q(hardback)
020 9780521056861|q(paper)
040 UkCbUP|beng|erda|cUkCbUP|dGP
041 0 eng
050 4 QA177|b.A83 1994
082 04 512.2|220
100 1 Aschbacher, Michael,|d1944-|eauthor
245 10 Sporadic groups /|cMichael Aschbacher
264 1 Cambridge :|bCambridge University Press,|c1994
300 1 online resource (xii, 314 pages) :|bdigital, PDF file(s)
336 text|btxt|2rdacontent
337 unmediated|bn|2rdamedia
338 volume|bnc|2rdacarrier
347 text file|bPDF|2rda
490 1 Cambridge tracts in mathematics ;|v104
500 Title from publisher's bibliographic system (viewed on 05
Oct 2015)
505 2 1. Preliminary Results -- 2. 2-Structure in Finite Groups
-- 3. Algebras, Codes, and Forms -- 4. Symplectic 2-Loops
-- 5. The Discovery, Existence, and Uniqueness of the
Sporadics -- 6. The Mathieu Groups, Their Steiner Systems,
and the Golay Code -- 7. The Geometry and Structure of
M[subscript 24] -- 8. The Conway Groups and the Leech
Lattice -- 9. Subgroups of [actual symbol not
reproducible] -- 10. The Griess Algebra and the Monster --
11. Subgroups of Groups of Monster Type -- 12. Coverings
of Graphs and Simplicial Complexes -- 13. The Geometry of
Amalgams -- 14. The Uniqueness of Groups of Type
M[subscript 24], He, and L[subscript 5](2) -- 15. The
Group U[subscript 4](3) -- 16. Groups of Conway, Suzuki,
and Hall-Janko Type -- 17. Subgroups of Prime Order in
Five Sporadic Groups
520 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
650 0 Sporadic groups (Mathematics)
830 0 Cambridge tracts in mathematics ;|v104
856 40 |uhttps://doi.org/10.1017/CBO9780511665585