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Author(s): | Daniel Gorenstein, Richard Lyons, Ronald Solomon | |||
Collection: | AMS survey 40 | |||
Publisher: | American Mathematical Society | |||
Year: | 1995 | |||
Language: | English | |||
Pages: | 176 pages | |||
Size: | 1.21 MB | |||
Extension: | DJVU | |||
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[content title="Description"] This book 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. 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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[content title="About the author"]Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician. He earned his undergraduate and graduate degrees at Harvard University, where he earned his Ph.D. in 1950 under Oscar Zariski, introducing in his dissertation a duality principle for plane curves that motivated Grothendieck's introduction of Gorenstein rings. He was a major influence on the classification of finite simple groups.Ronald "Ron“ Mark Solomon (b. 15 December 1948[1]) is an American mathematician specializing in the theory of finite groups.
Solomon studied as an undergraduate at Queens College and received a PhD in 1971 at Yale University under Walter Feit with a thesis entitled Finite Groups with Sylow 2-Subgroups of the Type of the Alternating Group on Twelve Letters. In 1972 he began his participation in the classification program for finite simple groups, after hearing a lecture by Daniel Gorenstein. He was for two years an instructor at the University of Chicago and the academic year 1974–1975 at Rutgers University, before he became a professor at Ohio State University, where he has remained. In 2006 he received the Levi L. Conant Prize and in 2012 the Leroy P. Steele Prize. In 2012 he was elected a Fellow of the American Mathematical Society.
With Gorenstein and Richard Lyons he wrote a series of six volumes on the classification program for finite simple groups in the context of a project for the examination of the proof.
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