Groups St Andrews 2001 in Oxford: Volume 2 (London Mathematical Society Lecture Note Series, Series Number 305)

This second 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 Peter Palfy (Eotvos Lorand, Budapest) and Michael Vaughan-Lee (Oxford). 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. Series-title......Page 3 Title......Page 5 Copyright......Page 6 Contents of Volume 2......Page 7 Contents of Volume 1......Page 9 INTRODUCTION......Page 13 1 Introduction......Page 15 2 Regular factorization and labeling of the vertices of a graph by group elements......Page 16 3 Regular Oberwolfach problems and group sequencings......Page 19 4 Transitive large sets of disjoint decompositions and group se-quencings......Page 20 5 Inner transitive Hering configurations......Page 23 References......Page 24 1 Introduction......Page 26 2 The numberof orbits......Page 27 3 The number of orbit sizes......Page 29 4 Large orbits......Page 34 5 The k(GV)–problem......Page 39 6 Orbits of permutation groups on the power set......Page 43 References......Page 46 1 Introduction......Page 52 2 Preliminaries on homologies of abelian groups with trivial coef-ficients and on the geometric invariant for modules over.........Page 53 3 More on the homology with coefficients in F......Page 54 4 Some results about homology......Page 59 5 Proof of Theorem A......Page 60 References......Page 63 1 Introduction......Page 64 2 Definitions of the geometric invariants and basic properties......Page 65 3 Groups acting on spaces......Page 67 4 Finite generation of modules and m-tameness......Page 69 5 Homological methods......Page 71 6.1 Basic properties of pro-p modules......Page 73 6.2 Homological finiteness properties of metabelian pro-p groups......Page 75 7 Homological properties of Lie algebras......Page 77 8 Valuation theory : link between the Lie, pro-p and discrete cases......Page 79 9 Related topics......Page 81 References......Page 83 1 Introduction......Page 86 References......Page 96 ON SOME INFINITE DIMENSIONAL LINEAR GROUPS......Page 97 References......Page 104 2 Preliminaries......Page 105 3 Bi-coset graph......Page 108 4 Main results......Page 111 5 Problems......Page 113 References......Page 114 1 Minimal covers......Page 115 2 Covers with conjugate subgroups......Page 117 3 Hall covers......Page 118 References......Page 119 Lemma 1......Page 120 Locally Graded Groups......Page 122 References......Page 123 1 Introduction......Page 125 2 The existence of N pie -injectors......Page 126 3 Abound of the number of conjugacy classes relatively to the class Npie......Page 128 References......Page 130 2 Bounding the derived length and the nilpotence class......Page 132 3 Minimal characters and normal subgroups......Page 134 4 Miscellaneous questions......Page 136 5 Character degrees of Sylow p-subgroups......Page 137 References......Page 140 1 Introduction......Page 142 2 Loops, groups and transversals......Page 143 3 Nilpotent and solvable loops......Page 144 References......Page 146 1 Introduction......Page 148 2 Overview......Page 149 3 Local stucture......Page 154 4 Laws in normal subgroup lattices......Page 161 5 Distributive normal subgroup lattices......Page 167 6 Subgroup lattices of direct powers......Page 169 References......Page 172 1 Introduction and preliminary results......Page 175 2 The long relator case......Page 182 3 TheTsaranov cases......Page 201 References......Page 205 1 Introduction......Page 207 2 Isaacs’s result on algebra groups......Page 208 3 Sylowp-subgroups of the classical groups as strong subgroups......Page 209 4 Classical groups in even characteristic......Page 211 References......Page 213 CHARACTER CORRESPONDENCES AND PERFECT ISOMETRIES......Page 214 References......Page 215 2 Notation......Page 216 3.2 Collections of the classes B......Page 217 3-2.2 Collection of the classes B......Page 218 3-2.3 Collection of the classes B......Page 219 3-2.5 Collection of classes B......Page 220 3-2.8 Collection of classes B......Page 221 3-3 Collection of the classes C and C......Page 222 4 Table of conjugacy classes and characters......Page 223 5 Appendix......Page 240 1 Introduction......Page 248 2 The elementary abelian group of automorphisms......Page 249 3 On the structure of periodic compact groups......Page 251 4 On centralizers in locally finite groups......Page 252 5 Exponent of a group with a single automorphism......Page 253 References......Page 255 1 Introduction......Page 257 2.2 Second: Given...describe the representations......Page 260 3.1 First: Define and compute Clif.........Page 261 3.3 Third: For each...calculate.........Page 263 4 Global methods......Page 264 References......Page 265 1 The Baker-Campbell-Hausdorff formula......Page 267 1.1 An example......Page 272 1.2 Justification......Page 276 1.3 Groups of class 2p - 2......Page 279 2 Torsion in outer commutator varieties......Page 280 3 Lie relators in varieties of groups......Page 288 3.1 Wall’s theory of multilinear Lie relators......Page 289 3.2 Burnside varieties......Page 291 4 Superalgebras......Page 298 References......Page 304 1 Composition algebras and Paige loops......Page 306 2 Multiplication versus addition......Page 308 3 Doubling triples......Page 310 4 Restrictions and Eextensions of automorphisms......Page 311 5 Automorphisms of finite octonion algebras......Page 312 6 Transitivity of the natural action......Page 314 7 Main result......Page 316 References......Page 317 Vol. 1. Permutabiity And Subnormality In Finite Groups/m.j. Alejandre -- (pro)-finite And (topologically) Locally Finite Groups With A Cc-subgroup/z. Arad -- Table Algebras Generated By Elements Of Small Degrees/a. Arad -- Subgroupgs Which Are A Union Of A Given Number Of Conjugacy Classes/a.r. Ashrafi -- Some Results On Finite Factorized Groups/a. Ballester-bolinches -- On Nilpotent-like Fitting Formations/a. Ballester-bolinches -- Locally Finite Groups With Min-p For All Primes P/a. Ballester-bolinches -- Quasi-permutation Representations Of 2-groups Of Class 2 With Cyclic Centre/h. Behravesh -- Groups Acting On Bordered Klein Surfaces With Maximal Symmetry/e. Bujalance -- Breaking Points In Subgroup Lattices/g. Calugareanu -- Group Actions On Graphs, Maps And Surfaces With Maximum Symmetry/m.d.e. Conder -- On Dual Pronormal Subgroups And Fitting Classes/a.d'aniello -- (p, Q, R)-generations Of The Sporadic Group O'n/m.r. Darafsheh -- Computations With Almost-crystallographic Groups/k. Dekimpe -- Random Walks On Groups: Characters And Geometry/p. Diaconis -- On Distances Of 2-groups And 3-groups/a. Drápal -- Zeta Functions Of Groups: The Quest For Order Versus The Flight From Ennui/m.p.f. Du Sautoy -- Some Factorizations Involving Hypercentrally Embedded Subgroups In Finite Soluble Groups/l.m. Ezquerro -- Elementary Theory Of Groups/b. Fine -- Andrews-curtis And Todd-coxeter Proof Words/g. Havas -- Short Balanced Presentations Of Perfect Groups/g. Havas -- Finte P-extensions Of Free Pro-p Groups/w. Herfort -- Elements And Groups Of Finite Length/m. Herzog -- Logged Rewriting And Identities Among Relators/a. Heyworth -- A Characterization Of F4(q) Where Q Is An Odd Prime Power/a. Iranmanesh -- On Associated Groups Of Rings/y.b. Ishchuk Vol. 2. Gracefulness, Group Sequencings And Graph Factorizations/g. Kaplan -- Orbits In Finite Group Actions/t.m. Keller -- Groups With Finitely Generated Integral Homologies/d.h. Kochloukova -- Invariants Of Discrete Groups, Lie Algebras And Pro-p Groups/d.h. Kochloukova -- Groups With All Non-subnormal Subgroups Of Finite Rank/l.a. Kurdachenko -- On Some Infinite Dimensional Linear Groups/l.a. Kurdachenko -- Groups And Semisymmetric Graphs/s. Lipschutz -- On The Covers Of The Finite Groups/m.s. Lucido -- Groupland/o. Macedonska -- On Maximal Nilpotent [pi]-subgroups/j. Medina -- Characters Of P-groups And Sylow P-subgroups/a. Moretó -- On The Relation Between Group Theory And Loop Theory/m. Niemenmaa -- Groups And Lattiices/p.p. Pálfy -- Finite Generalized Tetrahedron Groups With A Cubic Relator/g. Rosenberger -- Character Degrees Of The Sylow P-subgroups Of Classical Groups/j. Sangroniz -- Character Correspondences And Perfect Isometries/l. Sanus -- The Characters Of Finite Projective Symplectic Group Psp(4, Q) -- M.a. Shahabi -- Exponent Of Finite Groups With Automorphisms/p. Shumyatsky -- Classifying Irreducible Representations In Characteristic Zero/a. Turull -- Lie Methods In Group Theory/m.r. Vaughan-lee -- Chevalley Grops Of Type G2 As Automorphism Groups Of Loops/p. Vojtechovsky Edited By C.m. Campbell, E.f. Robertson, G.c. Smith. Includes Bibliographical References. 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 This two-volume set contains selected papers from the conference Groups St. Andrews 2001 in Oxford. Contributed by leading researchers, the articles cover a wide spectrum of modern group theory. Contributions based on lecture courses given by five main speakers are included with refereed survey and research articles. The Groups St. Andrews proceedings volumes represent a view of the state of the art in group theory and often play an important role in future developments in the subject. In this article we survey recent results on the connection between decompositions of complete graphs which admit given automorphism groups, and some combinatorial problems related to these groups.