Groups St Andrews 2001 in Oxford

doi:10.1017/CBO9780511542770

This first volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five 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 from Marston Conder (Auckland), Persi Diaconis (Stanford) and Marcus Du Sautoy (Cambridge). The series of Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past twenty years. As with earlier volumes, these refereed volumes also contain accessible surveys of contemporary research fronts, as well as a diverse collection of short research articles. They form a valuable reference for researchers, especially graduate students, working in group theory.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vii
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Contents of Volume 2
pp viii-x
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Introduction
pp xi-xii
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Permutability and subnormality in finite groups
pp 1-5
- By Manuel J. Alejandre, Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. del Ferrocarril s/n, 03202 Elche, Spain, A. Ballester-Bolinches, Departament d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain, R. Esteban-Romero, Departamento de Matemática Aplicada, E.U.I., Universidad Politécnica de Valencia, Camino de Vera, s/n, 46071 Valencia, Spain, M. C. Pedraza-Aguilera, Departamento de Matemática Aplicada, E.U.I., Universidad Politécnica de Valencia, Camino de Vera, s/n, 46071 Valencia, Spain; The work of the second and last authors is supported by Proyecto PB97-0674-C02-02 of DGICYT, MEC, Spain
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(Pro)-finite and (topologically) locally finite groups with a CC-subgroup
pp 6-11
- By Z. Arad, Department of Mathematics, Bar–Ilan University, Ramat–Gan, Israel and Department of Computer Science and Mathematics, Netanya Academic College, Netanya, Israel, W. Herfort, Institut für Angewandte und Numerische Mathematik, Technische Universität Vienna, Austria; The second author would like to thank for greatful hospitality at the Bar-Ilan University, the Netanya Academic College and the Tel-Aviv University in February 2000
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Table algebras generated by elements of small degrees
pp 12-21
- By Zvi Arad, Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel; Department of Computer Sciences and Mathematics Netanya Academic College, Netanya, 42365, Israel, Mikhail Muzychuk, Department of Computer Sciences and Mathematics Netanya Academic College, Netanya, 42365, Israel; The second author was supported by the Israeli Ministry of Absorption.
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Subgroups which are a union of a given number of conjugacy classes
pp 22-26
- By Ali Reza Ashrafi, Department of Mathematics, University of Kashan, Kashan, Iran, E-mail: ashrafi@kashanu.ac.ir, Heydar Sahraei, Department of Mathematics, University of Kashan, Kashan, Iran, E-mail: ashrafi@kashanu.ac.ir
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Some results on finite factorized groups
pp 27-30
- By A. Ballester-Bolinches, Departament d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain, John Cossey, Mathematics Department, School of Mathematical Sciences, The Australian National University, Canberra, 0200, Australia, Xiuyun Guo, Department of Mathematics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China, M. C. Pedraza-Aguilera, Departamento de Matemática Aplicada, E.U.I., Universidad Politécnica de Valencia, Camino de Vera, s/n, 46071 Valencia, Spain; The work of the first and last authors is supported by Proyecto PB97-0674-C02-02 of DGICYT, MEC, Spain
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On nilpotent-like Fitting formations
pp 31-38
- By A. Ballester-Bolinches, Departament d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain, A. Martínez-Pastor, Escuela Universitaria de Informática, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46071 Valencia, Spain, M.C. Pedraza-Aguilera, Escuela Universitaria de Informática, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46071 Valencia, Spain, M.D. Pérez-Ramos, Departament d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain; This research has been supported by Proyecto PB 97-0674-C02-02 of DGICYT, Ministerio de Educación y Ciencia, Spain.
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Locally finite groups with min-p for all primes p
pp 39-43
- By A. Ballester-Bolinches, Departament d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain, Tatiana Pedraza, Departament d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain; This work is supported by Proyecto PB97-0674-C02-02 of DGICYT, MEC, Spain
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Quasi-permutation representations of 2-groups of class 2 with cyclic centre
pp 44-49
- By Houshang Behravesh, Department of Mathematics, University of Urmia, Urmia, Iran, Email: h.behravesh@mail.urmia.ac.ir; Institute for Studies in Theoretical Physics and Mathematics, P.O.Box 19395-5746, Tehran, Iran
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Groups acting on bordered Klein surfaces with maximal symmetry
pp 50-58
- By Emilio Bujalance, Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, Madrid 28040, Spain, E-mail: eb@mat.uned.es and jcirre@mat.uned.es, Francisco Javier Cirre, Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, Madrid 28040, Spain, E-mail: eb@mat.uned.es and jcirre@mat.uned.es, Peter Turbek, Department of Mathematics, Computer Science and Statistics, Purdue University Calumet, Hammond, Indiana, 46323, U.S.A., Email: turbek@nwi.calumet.purdue.edu; The first author is partially supported by DGICYT PB98-0017 and the second author is partially supported by DGICYT PB98-0756.
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Breaking points in subgroup lattices
pp 59-62
- By Grigore Calugareanu, Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait, Marian Deaconescu, Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait; The second named author wishes to thank Kuwait University for financial support through research contract SM09/00.
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Group actions on graphs, maps and surfaces with maximum symmetry
pp 63-91
- By Marston Conder, Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
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On dual pronormal subgroups and Fitting classes
pp 92-100
- By A. D'Aniello, Dipartimento di Matematica e Applicazioni. Università di Napoli, Via Claudio 21, 80125 Napoli (Italia), M.D. Pérez-Ramos, Departament d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain; Supported by Proyecto PB 97-0674-C02-02 of DGICYT, Ministerio de Educación y Ciencia, Spain.
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(p, q, r)-generations of the sporadic group O'N
pp 101-109
- By M. R. Darafsheh, Department of Mathematics and Computer Science, University of Tehran, Tehran, Iran, E-mail: daraf@khayam.ut.ac.ir, A. R. Ashrafi, Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran, E-mail: ashrafi@kashanu.ac.ir, G. A. Moghani, Department of Mathematics, Iran University of Science and Technology, Tehran, Iran, E-mail: moghani@iust.ac.ir.
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Computations with almost-crystallographic groups
pp 110-119
- By Karel Dekimpe, Katholieke Universiteit Leuven, Campus Kortrijk, B–8500 Kortrijk, Belgium, Bettina Eick, Fachbereich für Mathematik, Universität Kassel, D–34109 Kassel, Germany
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Random walks on groups: characters and geometry
pp 120-142
- By Persi Diaconis, Departments of Mathematics and Statistics, Stanford University, Stanford, CA 94305 USA
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On distances of 2-groups and 3-groups
pp 143-149
- By Aleš Drápal, Department of Mathematics, Charles University, Sokolovská 83, 186 75 Prague, Czech Rep.; Work supported by institutional grant MSM 113200007, and by Grant Agency of Charles University, grant 269/2001/B-MAT/MFF.
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Zeta functions of groups: the quest for order versus the flight from ennui
pp 150-189
- By Marcus Du Sautoy, Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB, UK, E-mail: dusautoy@maths.ox.ac.uk, URL http://www.maths.ox.ac.uk/∼dusautoy
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Some factorizations involving hypercentrally embedded subgroups in finite soluble groups
pp 190-196
- By L. M. Ezquerro, Departamento de Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía. 31006 Pamplona, Spain, X. Soler-Escrivá, Centre d'Investigació Operativa, Departament d'Estadística y Matemàtica Aplicada, Universitat Miguel Hernández, Avinguda del Ferrocarril, s/n. 03202 Elx, Spain, E-mail: xaro@umh.es
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Elementary theory of groups
pp 197-231
- By Benjamin Fine, Department of Mathematics, Fairfield University, Fairfield, Connecticut 06430, USA, Anthony M. Gaglione, Department of Mathematics, U.S. Naval Academy, Anapolis, Maryland 1402, USA, Alexei Myasnikov, Department of Mathematics, City College of CUNY, New York, New York 10031, USA, Gerhard Rosenberger, Fachbereich Mathematik Universität, Dortmund, 44221 Dortmund, Germany, Dennis Spellman, Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19132, USA
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Andrews-Curtis and Todd-Coxeter proof words
pp 232-237
- By George Havas, School of Computer Science and Electrical Engineering, The University of Queensland, Queensland 4072, Australia Email: havas@csee.uq.edu.au and cram@csee.uq.edu.au, Colin Ramsay, School of Computer Science and Electrical Engineering, The University of Queensland, Queensland 4072, Australia Email: havas@csee.uq.edu.au and cram@csee.uq.edu.au; Both authors were partially supported by the Australian Research Council
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Short balanced presentations of perfect groups
pp 238-243
- By George Havas, Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland, Queensland 4072,Australia, Email: havas@itee.uq.edu.au and cram@itee.uq.edu.au, Colin Ramsay, Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland, Queensland 4072,Australia, Email: havas@itee.uq.edu.au and cram@itee.uq.edu.au; Both authors were partially supported by the Australian Research Council
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Finite p-extensions of free pro-p groups
pp 244-248
- By W. Herfort, University of Technology, Vienna, Austria; The first author would like to thank for generous support and greatful hospitality at the University of Brasilia during stays July-August in 1999 and 2000, P. A. Zalesskii, University of Brasilia, Brazil; The second author acknowledges the financial support of CNPq
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Elements and groups of finite length
pp 249-255
- By Marcel Herzog, School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel; The first author is grateful to the Department of Mathematics of the University of Hawaii at Manoa for its hospitality and support, while this investigation was carried out., Patrizia Longobardi, Dipartimento di Matematica e Informatica Università di Salerno via Salvator Allende, 84081 Baronissi(Salerno), Italy, Mercede Maj, Dipartimento di Matematica e Informatica Università di Salerno via Salvator Allende, 84081 Baronissi(Salerno), Italy
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Logged rewriting and identities among relators
pp 256-276
- By Anne Heyworth, Department of Mathematics and Computer Science, University of Leicester, LE1 7RH UK; Supported by EPSRC grant GR/R29604/01 Kan: A Categorical Approach to Computer Algebra, Christopher D. Wensley, Department of Informatics, Mathematics Division, University of Wales, Bangor, LL57 1UT, UK
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A characterization of F4(q) where q is an odd prime power
pp 277-283
- By A. Iranmanesh, Department of Mathematics, Tarbiat Modarres University, P.O. Box: 14115-137, Tehran, Iran, E-mail: iranman@vax.ipm.ac.ir, B. Khosravi, Center for Theoretical Physics and Mathematics P.O. Box 11365-8486, AEOI, Tehran, Iran
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On associated groups of rings
pp 284-293
- By Yurii Ishchuk, Department of Mechanics and Mathematics, Ivan Franko National University of Lviv, Universytetska, 1, Lviv 79000, Ukraine, E-mail: topos@franko.lviv.ua
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Groups St Andrews 2001 in Oxford

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