Groups St Andrews 2001 in Oxford: Volume 2

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