An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
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
List Price: $68.00 MAA Member Price:$61.20
AMS Member Price: $40.80 Click above image for expanded view 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  List Price:$68.00 MAA Member Price: $61.20 AMS Member Price:$40.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 2032009; 74 pp
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
• Request Review Copy
• Get Permissions
Volume: 2032009; 74 pp
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
Please select which format for which you are requesting permissions.