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Classical Groups, Derangements and Primes

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Title: Classical Groups, Derangements and Primes
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.
Authors: Timothy C. Burness, Michael Giudici
Resource Type: eBook.
Subjects: Numbers, Prime, Algebra, Logic, Symbolic and mathematical, Group theory
Categories: MATHEMATICS / Algebra / General
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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DbLabel: eBook Collection (EBSCOhost)
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PubType: eBook
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  Data: Classical Groups, Derangements and Primes
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  Label: Description
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  Data: 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.
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  Data: <searchLink fieldCode="AR" term="%22Timothy+C%2E+Burness%22">Timothy C. Burness</searchLink><br /><searchLink fieldCode="AR" term="%22Michael+Giudici%22">Michael Giudici</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Numbers%2C+Prime%22">Numbers, Prime</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Logic%2C+Symbolic+and+mathematical%22">Logic, Symbolic and mathematical</searchLink><br /><searchLink fieldCode="DE" term="%22Group+theory%22">Group theory</searchLink>
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      – Code: 512.7
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Numbers, Prime
        Type: general
      – SubjectFull: Algebra
        Type: general
      – SubjectFull: Logic, Symbolic and mathematical
        Type: general
      – SubjectFull: Group theory
        Type: general
    Titles:
      – TitleFull: Classical Groups, Derangements and Primes
        Type: main
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          Name:
            NameFull: Timothy C. Burness
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            NameFull: Michael Giudici
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            NameFull: Timothy C. Burness
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            NameFull: Michael Giudici
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2016
            – D: 19
              M: 01
              Type: profile
              Y: 2016
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              Value: 9781107629448
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              Value: 9781316439777
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            – Type: volume
              Value: 00025
          Titles:
            – TitleFull: Classical Groups, Derangements and Primes
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