Groups St Andrews 2005

doi:10.1017/CBO9780511721212

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Volume 1
Edited by C. M. Campbell, University of St Andrews, Scotland, M. R. Quick, University of St Andrews, Scotland, E. F. Robertson, University of St Andrews, Scotland, G. C. Smith, University of Bath

Publisher:: Cambridge University Press
Online publication date:: May 2010
Print publication year:: 2007
Online ISBN:: 9780511721212
DOI:: https://doi.org/10.1017/CBO9780511721212

Subjects:: Mathematics (general), Mathematics, Algebra
Series:: London Mathematical Society Lecture Note Series (339)

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'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.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-viii
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Introduction
pp ix-x
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Aspects of infinite permutation groups
pp 1-35
- By Peter J. Cameron, School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
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Self-similarity and branching in group theory
pp 36-95
- By Rostislav Grigorchuk, Department of Mathematics, Texas A&M University, MS–3368, College Station, TX 77843–3368, USA, Zoran Šunić
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On surface groups: motivating examples in combinatorial group theory
pp 96-129
- By Peter Ackermann, Peter Ackermann, Fachbereich Mathematik, Universitat Dortmund, 44227 Dortmund, Federal Republic of Germany, Benjamin Fine, Department of Mathematics, Fairfield University, Fairfield, Connecticut 06430, United States, Gerhard Rosenberger, Fachbereich Mathematik, Universitat Dortmund, 44227 Dortmund, Federal Republic of Germany
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Nilpotent p-algebras and factorized p-groups
pp 130-148
- By Bernhard Amberg, Institut für Mathematik, Johannes-Gutenberg-Universität, 55099 Mainz, Germany, Lev Kazarin, Department of Mathematics, Yaroslavl State University, 150000 Yaroslavl, Russia
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Classification of finite groups by the number of element centralizers
pp 149-157
- By Ali Reza Ashrafi, Department of Mathematics, University of Kashan, Kashan, Iran, Bijan Taeri, Department of Mathematics, Isfahan University of Technology, Isfahan, Iran
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Algorithmic use of the Mal'cev correspondence
pp 158-169
- By Björn Assmann, Centre for Interdisciplinary Research in Computational Algebra (CIRCA), University of St Andrews, North Haugh, St Andrews, KY16 9SS Fife, Scotland
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Minimal but inefficient presentations for semi-direct products of finite cyclic monoids
pp 170-185
- By Firat Ateş, Balikesir Universitesi, Fen-Edebiyat Fakultesi, Matematik Bolumu, 10100 Balikesir/Turkey, A. Sinan Çevik
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The modular isomorphism problem for finite p-groups with a cyclic subgroup of index p2
pp 186-193
- By Czesław Bagiński, Institute of Computer Science, Technical University of Bialystok, Wiejska 45A, 15–351 Bialystok, Poland, Alexander Konovalov, Department of Mathematics, Zaporozhye National University, Zhukovskogo street, 66, Zaporozhye, 69063, Ukraine
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On one-generated formations
pp 194-198
- By A. Ballester-Bolinches, Departament d'Álgebra, Universitat de Valéncia, Dr. Moliner, 50, 46100 Burjassot (Valéncia), Spain, Clara Calvo, R. Esteban-Romero, Departament de Matemática Aplicada-IMPA, Universitat Politécnica de Valéncia, Camí de Vera, s/n, 46022 Valéncia, Spain
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New results on products of finite groups
pp 199-202
- By A. Ballester-Bolinches, Departament d'Àlgebra, Universitat de Valéncia, C/ Doctor Moliner 50, 46100 Burjassot (Valéncia), Spain, John Cossey, Mathematics Department, School of Mathematical Sciences, The Australian National University, Canberra, 0200, Australia, M. C. Pedraza-Aguilera, ETS de Informática Aplicada, Departamento de Matemática Aplicada-IMPA, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain
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Radical locally finite T-groups
pp 203-206
- By A. Ballester-Bolinches, Departament d'Álgebra, Universitat de Valéncia, c/ Doctor Moliner 50, 46100 Burjassot (Valencia), Spain, H. Heineken, Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany, Tatiana Pedraza, ETS de Informática Aplicada, Departamento de Matemática Aplicada-IMPA, Universidad Politécnica de Valencia, 46022 Valencia, Spain
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Explicit tilting complexes for the Broué conjecture on 3-blocks
pp 207-223
- By Ayala Bar-Ilan, Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel, Tzviya Berrebi, Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel, Genadi Chereshnya, Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel, Ruth Leabovich, Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel, Mikhal Cohen, Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel, Mary Schaps, Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel
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Conjugacy classes of p-regular elements in p-solvable groups
pp 224-229
- By Antonio Beltrán, Departament de matemátiques, Universitat Jaume I de Castlló, Av. Sos Baynat s/n, 12071 Castellón, Spain, María José Felipe, Departamento de Matemática Aplicada-IMPA, Universidad Politécnica de Valencia, C/ Camino de Vera s/n, 46022 Valencia, Spain
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An algorithm for the unit group of the Burnside ring of a finite group
pp 230-236
- By Robert Boltje, Department of Mathematics, University of California, Santa Cruz, CA 95064, U.S.A., Götz Pfeiffer, National University of Ireland, Galway, Ireland
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Integral group ring of the first Mathieu simple group
pp 237-245
- By Victor Bovdi, Institute of Mathematics, University of Debrecen, P.O. Box 12, H–4010 Debrecen; Institute of Mathematics and Informatics, College of Nyíregyháza, Sóstói út 31/b, H–4410 Nyíregyháaza, Hungary, Alexander Konovalov, Department of Mathematics, Zaporozhye National University, 66 Zhukovskogo str., 69063, Zaporozhye, Ukraine; current address: Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, B–1050 Brussel, Belgium
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Embedding properties in direct products
pp 246-255
- By B. Brewster, Department of Mathematical Sciences, Binghamton University-SUNY, Binghamton, NY 13902–6000, U.S.A., A. Martínez-Pastor, Escuela Técnica Superior de Informática Aplicada, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain, M. D. Pérez-Ramos, Departament d'Álgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain
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Malcev presentations for subsemigroups of groups — a survey
pp 256-268
- By Alan J. Cain, School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, United Kingdom
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Finite groups with extremal conditions on sizes of conjugacy classes and on degrees of irreducible characters
pp 269-273
- By David Chillag, Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel, Marcel Herzog, School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel
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Conjugacy class structure in simple algebraic groups
pp 274-287
- By Martin Cook, Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, United Kingdom
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On automorphisms of products of groups
pp 288-305
- By Jill Dietz, Department ofMathematics, Statistics, and Computer Science, St. Olaf College, Northfield, MN 55057, U.S.A.
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Linear groups with infinite central dimension
pp 306-312
- By Martyn R. Dixon, Department of Mathematics, University of Alabama Tuscaloosa, AL 35487–0350, U.S.A., Leonid A. Kurdachenko, Department of Algebra, University of Dnepropetrovsk, Vulycya Naukova 13, Dnepropetrovsk 50, 49050, Ukraine
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G-automata, counter languages and the Chomsky hierarchy
pp 313-318
- By Murray Elder, School of Mathematics and Statistics, University of St Andrews, Scotland
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An embedding theorem for groups universally equivalent to free nilpotent groups
pp 319-326
- By Benjamin Fine, Anthony M. Gaglione, Dennis Spellman
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Irreducible word problems in groups
pp 327-340
- By Ana R. Fonseca, Department of Computer Science, University of Leicester, Leicester LE1 7RH, England, Duncan W. Parkes, Department of Computer Science, University of Leicester, Leicester LE1 7RH, England, Richard M. Thomas, Department of Computer Science, University of Leicester, Leicester LE1 7RH, England
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Recent growth results
pp 341-355
- By Eric M. Freden, Southern Utah University, Cedar City UT, U.S.A., Teresa Knudson
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Groups St Andrews 2005

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Introduction
pp ix-x

Aspects of infinite permutation groups
pp 1-35

Self-similarity and branching in group theory
pp 36-95

On surface groups: motivating examples in combinatorial group theory
pp 96-129

Nilpotent p-algebras and factorized p-groups
pp 130-148

Classification of finite groups by the number of element centralizers
pp 149-157

Algorithmic use of the Mal'cev correspondence
pp 158-169

Minimal but inefficient presentations for semi-direct products of finite cyclic monoids
pp 170-185

The modular isomorphism problem for finite p-groups with a cyclic subgroup of index p2
pp 186-193

On one-generated formations
pp 194-198

New results on products of finite groups
pp 199-202

Radical locally finite T-groups
pp 203-206

Explicit tilting complexes for the Broué conjecture on 3-blocks
pp 207-223

Conjugacy classes of p-regular elements in p-solvable groups
pp 224-229

An algorithm for the unit group of the Burnside ring of a finite group
pp 230-236

Integral group ring of the first Mathieu simple group
pp 237-245

Embedding properties in direct products
pp 246-255

Malcev presentations for subsemigroups of groups — a survey
pp 256-268

Finite groups with extremal conditions on sizes of conjugacy classes and on degrees of irreducible characters
pp 269-273

Conjugacy class structure in simple algebraic groups
pp 274-287

On automorphisms of products of groups
pp 288-305

Linear groups with infinite central dimension
pp 306-312

G-automata, counter languages and the Chomsky hierarchy
pp 313-318

An embedding theorem for groups universally equivalent to free nilpotent groups
pp 319-326

Irreducible word problems in groups
pp 327-340

Recent growth results
pp 341-355

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