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Regular Subgroups of Primitive Permutation Groups
 
Martin W. Liebeck Imperial College, London, England
Cheryl E. Praeger University of Western Australia, Crawley, Australia
Jan Saxl University of Cambridge, Cambridge, England
Front Cover for Regular Subgroups of Primitive Permutation Groups
Available Formats:
Electronic ISBN: 978-1-4704-0566-3
Product Code: MEMO/203/952.E
74 pp 
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
Front Cover for Regular Subgroups of Primitive Permutation Groups
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  • Front Cover for Regular Subgroups of Primitive Permutation Groups
  • Back Cover for Regular Subgroups of Primitive Permutation Groups
Regular Subgroups of Primitive Permutation Groups
Martin W. Liebeck Imperial College, London, England
Cheryl E. Praeger University of Western Australia, Crawley, Australia
Jan Saxl University of Cambridge, Cambridge, England
Available Formats:
Electronic ISBN:  978-1-4704-0566-3
Product Code:  MEMO/203/952.E
74 pp 
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2032009
    MSC: Primary 20; 05;

    The authors address the classical problem of determining finite primitive permutation groups \(G\) with a regular subgroup \(B\). The main theorem solves the problem completely under the assumption that \(G\) is almost simple. While there are many examples of regular subgroups of small degrees, the list is rather short (just four infinite families) if the degree is assumed to be large enough, for example at least 30!. Another result determines all primitive groups having a regular subgroup which is almost simple. This has an application to the theory of Cayley graphs of simple groups.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Transitive and antiflag transitive linear groups
    • 4. Subgroups of classical groups transitive on subspaces
    • 5. Proof of Theorem 1.1: Linear groups
    • 6. Proof of Theorem 1.1: Unitary groups
    • 7. Proof of Theorem 1.1: Orthogonal groups in odd dimension
    • 8. Proof of Theorem 1.1: Orthogonal groups of minus type
    • 9. Proof of Theorem 1.1: Some special actions of symplectic and orthogonal groups
    • 10. Proof of Theorem 1.1: Remaining symplectic cases
    • 11. Proof of Theorem 1.1: Orthogonal groups of plus type
    • 12. Proof of Theorem 1.1: Exceptional groups of Lie type
    • 13. Proof of Theorem 1.1: Alternating groups
    • 14. Proof of Theorem 1.1: Sporadic groups
    • 15. Proof of Theorem and Corollary
    • 16. The tables in Theorem
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Volume: 2032009
MSC: Primary 20; 05;

The authors address the classical problem of determining finite primitive permutation groups \(G\) with a regular subgroup \(B\). The main theorem solves the problem completely under the assumption that \(G\) is almost simple. While there are many examples of regular subgroups of small degrees, the list is rather short (just four infinite families) if the degree is assumed to be large enough, for example at least 30!. Another result determines all primitive groups having a regular subgroup which is almost simple. This has an application to the theory of Cayley graphs of simple groups.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Transitive and antiflag transitive linear groups
  • 4. Subgroups of classical groups transitive on subspaces
  • 5. Proof of Theorem 1.1: Linear groups
  • 6. Proof of Theorem 1.1: Unitary groups
  • 7. Proof of Theorem 1.1: Orthogonal groups in odd dimension
  • 8. Proof of Theorem 1.1: Orthogonal groups of minus type
  • 9. Proof of Theorem 1.1: Some special actions of symplectic and orthogonal groups
  • 10. Proof of Theorem 1.1: Remaining symplectic cases
  • 11. Proof of Theorem 1.1: Orthogonal groups of plus type
  • 12. Proof of Theorem 1.1: Exceptional groups of Lie type
  • 13. Proof of Theorem 1.1: Alternating groups
  • 14. Proof of Theorem 1.1: Sporadic groups
  • 15. Proof of Theorem and Corollary
  • 16. The tables in Theorem
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