The third of three volumes treating the generic case of the classification proof provides a complete proof of a theorem which assumes that p-thin configurations do not exist in G when the ?-proper simple group G is of generic type relative to the prime p. The set of target simple groups for the theorem consists of alternating groups. Lyons (Rutgers University) and Solomon (Ohio State University) explain recognition of Chevalley groups by Curtis-Tits systems and Phan systems, list possible neighborhoods and neighbors, and review computations in groups of Lie type. Annotation ©2019 Ringgold, Inc., Portland, OR (protoview.com)
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Condizione: New. This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach the comp. Codice articolo 274381549
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Hardback. Condizione: New. This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series--the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups.Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series. Codice articolo LU-9781470441890
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