Classical groups, derangements and primes

著者

    • Burness, Timothy C.
    • Giudici, Michael

書誌事項

Classical groups, derangements and primes

Timothy C. Burness, Michael Giudici

(Australian Mathematical Society lecture series, 25)

Cambridge University Press, 2016

  • : pbk

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注記

Includes bibliographical references (p. 339-344) and index

内容説明・目次

内容説明

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.

目次

  • Preface
  • Notational conventions
  • 1. Introduction
  • 2. Finite classical groups
  • 3. Conjugacy classes
  • 4. Subspace actions
  • 5. Non-subspace actions
  • 6. Low-dimensional classical groups
  • Appendix A. Number-theoretic miscellanea
  • Appendix B. Tables
  • References
  • Index.

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詳細情報

  • NII書誌ID(NCID)
    BB20630374
  • ISBN
    • 9781107629448
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    xviii, 346 p.
  • 大きさ
    23 cm
  • 分類
  • 件名
  • 親書誌ID
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