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Classical Groups, Derangements and Primes
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  • Cited by 6
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lee, Melissa and Liebeck, Martin 2018. Bases for quasisimple linear groups. Algebra & Number Theory, Vol. 12, Issue. 6, p. 1537.

    Burness, Timothy C. and Thomas, Adam R. 2018. On the involution fixity of exceptional groups of Lie type. International Journal of Algebra and Computation, Vol. 28, Issue. 03, p. 411.

    BURNESS, TIMOTHY C. and GIUDICI, MICHAEL 2018. On the Saxl graph of a permutation group. Mathematical Proceedings of the Cambridge Philosophical Society, p. 1.

    Spiga, Pablo 2017. On the number of derangements and derangements of prime power order of the affine general linear groups. Journal of Algebraic Combinatorics, Vol. 45, Issue. 2, p. 345.

    BAMBERG, JOHN POPIEL, TOMASZ and PRAEGER, CHERYL E. 2017. SIMPLE GROUPS, PRODUCT ACTIONS, AND GENERALIZED QUADRANGLES. Nagoya Mathematical Journal, p. 1.

    BURNESS, TIMOTHY C. and COVATO, ELISA 2015. ON THE PRIME GRAPH OF SIMPLE GROUPS. Bulletin of the Australian Mathematical Society, Vol. 91, Issue. 02, p. 227.

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Book description

A classical theorem of Jordan states that every finite transitive permutation group contains a derangement. This existence result has interesting and unexpected applications in many areas of mathematics, including graph theory, number theory and topology. Various generalisations have been studied in more recent years, with a particular focus on the existence of derangements with special properties. Written for academic researchers and postgraduate students working in related areas of algebra, this introduction to the finite classical groups features a comprehensive account of the conjugacy and geometry of elements of prime order. The development is tailored towards the study of derangements in finite primitive classical groups; the basic problem is to determine when such a group G contains a derangement of prime order r, for each prime divisor r of the degree of G. This involves a detailed analysis of the conjugacy classes and subgroup structure of the finite classical groups.

Reviews

'This book should be an indispensable reference for anybody doing research, or wanting to do research, in this area. Even for nonspecialists, however, chapters 2 and 3 should be a useful source of information on classical groups.'

Mark Hunacek Source: The Mathematical Gazette

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