Electronic ISBN:  9781470405663 
Product Code:  MEMO/203/952.E 
74 pp 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $40.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 203; 2009MSC: 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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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