Memoirs of the American Mathematical Society 2009; 74 pp; softcover Volume: 203 ISBN10: 082184654X ISBN13: 9780821846544 List Price: US$68 Individual Members: US$40.80 Institutional Members: US$54.40 Order Code: MEMO/203/952
 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  Introduction
 Preliminaries
 Transitive and antiflag transitive linear groups
 Subgroups of classical groups transitive on subspaces
 Proof of Theorem 1.1: Linear groups
 Proof of Theorem 1.1: Unitary groups
 Proof of Theorem 1.1: Orthogonal groups in odd dimension
 Proof of Theorem 1.1: Orthogonal groups of minus type
 Proof of Theorem 1.1: Some special actions of symplectic and orthogonal groups
 Proof of Theorem 1.1: Remaining symplectic cases
 Proof of Theorem 1.1: Orthogonal groups of plus type
 Proof of Theorem 1.1: Exceptional groups of Lie type
 Proof of Theorem 1.1: Alternating groups
 Proof of Theorem 1.1: Sporadic groups
 Proof of Theorem 1.4 and Corollary 1.3
 The tables in Theorem 1.1
 References
