Overview
- Authors:
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John D. Dixon
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Department of Mathematics and Statistics, Carleton University, Ottawa, Canada
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Brian Mortimer
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Department of Mathematics and Statistics, Carleton University, Ottawa, Canada
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Table of contents (9 chapters)
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- John D. Dixon, Brian Mortimer
Pages 1-32
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- John D. Dixon, Brian Mortimer
Pages 33-64
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- John D. Dixon, Brian Mortimer
Pages 65-105
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- John D. Dixon, Brian Mortimer
Pages 106-142
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- John D. Dixon, Brian Mortimer
Pages 143-176
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- John D. Dixon, Brian Mortimer
Pages 177-209
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- John D. Dixon, Brian Mortimer
Pages 210-254
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- John D. Dixon, Brian Mortimer
Pages 255-273
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- John D. Dixon, Brian Mortimer
Pages 274-301
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Back Matter
Pages 302-348
About this book
Permutation Groups form one of the oldest parts of group theory. Through the ubiquity of group actions and the concrete representations which they afford, both finite and infinite permutation groups arise in many parts of mathematics and continue to be a lively topic of research in their own right. The book begins with the basic ideas, standard constructions and important examples in the theory of permutation groups.It then develops the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal O'Nan-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. This text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, or for self- study. It includes many exercises and detailed references to the current literature.