Groups St Andrews 2005: Volume 1 (London Mathematical Society Lecture Note Series, Series Number 339)

'Groups St Andrews 2005' was held in the University of St Andrews in August 2005 and this first volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by Peter Cameron (Queen Mary, London) and Rostislav Grogorchuk (Texas A&M, USA). Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important. Cover......Page 1 Title Page......Page 4 Copyright......Page 5 Introduction......Page 0 Contents of Volume 1......Page 6 Contents of Volume 2......Page 8 Aspects of infinite permutation groups......Page 12 Self-similarity and branching in group theory......Page 47 On surface groups: motivating examples in combinatorial group theory......Page 107 Nilpotent p-algebras and factorized p-groups......Page 141 Classification of finite groups by the number of element centralizers......Page 159 Algorithmic use of the Mal'cev correspondence......Page 169 Minimal but inefficient presentations for semi-direct products of finite cyclic monoids......Page 181 The modular isomorphism problem for finite p-groups with a cyclic subgroup of index p^2......Page 197 On one-generated formations......Page 205 New results on products of finite groups......Page 210 Radical locally finite T-groups......Page 214 Explicit tilting complexes for the Brou?Le conjecture on 3-blocks......Page 218 Conjugacy classes of p-regular elements in p-solvable groups......Page 235 An algorithm for the unit group of the Burnside ring of a finite group......Page 241 Integral group ring of the first Mathieu simple group......Page 248 Embedding properties in direct products......Page 257 Malcev presentations for subsemigroups of groups --- a survey......Page 267 Finite groups with extremal conditions on sizes of conjugacy classes and on degrees of irreducible characters......Page 280 Conjugacy class structure in simple algebraic groups......Page 285 On automorphisms of products of groups......Page 299 Linear groups with infinite central dimension......Page 317 G-automata, counter languages and the Chomsky hierarchy......Page 324 An embedding theorem for groups universally equivalent to free nilpotent groups......Page 330 Irreducible word problems in groups......Page 338 Recent growth results......Page 352 'Groups St Andrews 2005' was held in the University of St Andrews in August 2005 and this first volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by Peter Cameron (Queen Mary, London) and Rostislav Grogorchuk (Texas A & M, USA). Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important This first volume of a two-volume book contains selected papers from the international conference 'Groups St Andrews 2005'. Contributions by Peter Cameron and Rostislav Grogorchuk are included, as are survey and research articles by other conference participants, to provide a snapshot of the state of research in group theory today. This second volume of a two-volume book contains selected papers from the international conference 'Groups St Andrews 2005'. Contributions by John Meakin and Ákos Seress are included, as are survey and research articles by other conference participants, to provide a snapshot of the state of research in group theory today.