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Permutation Groups (Graduate Texts in Mathematics)
 
 
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Permutation Groups (Graduate Texts in Mathematics) [Hardcover]

John D. Dixon (Author), Brian Mortimer (Author)

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Book Description

0387945997 978-0387945996 April 11, 1996 1
Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. With its many exercises and detailed references to the current literature, this text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, as well as for self-study.

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Inside This Book (learn more)
First Sentence:
A cube is highly symmetric: there are many ways to rotate or reflect it so that it moves onto itself. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite primitive group, minimal preimage, multiply transitive groups, regular socle, countable universal graph, nondiagonal orbital, permutation isomorphic, unique hyperoval, regular normal subgroup, transitive extension, primitive permutation groups, point stabilizer, permutation isomorphism, infinite symmetric groups, strong generating set, imprimitive group, primitive subgroup, twisted wreath product, nontrivial blocks, nonabelian simple group, regular subgroup, transitive subgroup, frobenius groups, finite permutation groups, subnormal subgroup
Key Phrases - Capitalized Phrases (CAPs): (learn more)
O'Nan-Scott Theorem, Nonregular Socles, O'Nan Scott Theorem, Use Exercise, The Basic Ideas, Evariste Galois, Jordan Witt Lemma
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