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＜電子ブック＞
Fundamental Algorithms for Permutation Groups / by Gregory Butler
(Lecture Notes in Computer Science. ISSN:16113349 ; 559)

版	1st ed. 1991.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1991
本文言語	英語
大きさ	XII, 244 p : online resource
著者標目	*Butler, Gregory author SpringerLink (Online service)
件　名	LCSH:Computer science LCSH:Group theory LCSH:Discrete mathematics LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Algorithms FREE:Theory of Computation FREE:Group Theory and Generalizations FREE:Discrete Mathematics FREE:Symbolic and Algebraic Manipulation FREE:Algorithms
一般注記	Group theory background -- List of elements -- Searching small groups -- Cayley graph and defining relations -- Lattice of subgroups -- Orbits and schreier vectors -- Regularity -- Primitivity -- Inductive foundation -- Backtrack search -- Base change -- Schreier-Sims method -- Complexity of the Schreier-Sims method -- Homomorphisms -- Sylow subgroups -- P-groups and soluble groups -- Soluble permutation groups -- Some other algorithms This is the first-ever book on computational group theory. It provides extensive and up-to-date coverage of the fundamental algorithms for permutation groups with reference to aspects of combinatorial group theory, soluble groups, and p-groups where appropriate. The book begins with a constructive introduction to group theory and algorithms for computing with small groups, followed by a gradual discussion of the basic ideas of Sims for computing with very large permutation groups, and concludes with algorithms that use group homomorphisms, as in the computation of Sylowsubgroups. No background in group theory is assumed. The emphasis is on the details of the data structures and implementation which makes the algorithms effective when applied to realistic problems. The algorithms are developed hand-in-hand with the theoretical and practical justification.All algorithms are clearly described, examples are given, exercises reinforce understanding, and detailed bibliographical remarks explain the history and context of the work. Much of the later material on homomorphisms, Sylow subgroups, and soluble permutation groups is new HTTP:URL=https://doi.org/10.1007/3-540-54955-2

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