Groups St Andrews 2001 in Oxford, Vol 1

Cover......Page 1
Series-title......Page 3
Title......Page 5
Copyright......Page 6
Contents of Volume 1......Page 7
Contents of Volume 2......Page 10
INTRODUCTION......Page 13
1 Notation and terminology......Page 15
3 Characterizations based on the Sylow structure......Page 16
4 Characterizations based on embedding properties......Page 18
References......Page 19
1.1 Sketching the thread......Page 20
2 Announcement of the results......Page 21
References......Page 24
1 Introduction......Page 26
1.1 Examples......Page 27
1.2 Wreath, tensor and fibred products......Page 28
2 Classification results about standard integral table algebras......Page 29
2.1 The algebras…......Page 31
2.2 The algebras…......Page 32
3 Normalized table algebras generated by a nonreal element of degree 3......Page 34
References......Page 35
1 Introduction......Page 36
2 On n-decomposable finite groups......Page 38
References......Page 40
SOME RESULTS ON FINITE FACTORIZED GROUPS......Page 41
References......Page 44
1 Introduction......Page 45
2 Lattice formations......Page 46
3 Formations with the Shemetkov property......Page 48
5 Dominant Fitting classes......Page 50
References......Page 52
LOCALLY FINITE GROUPS WITH MIN-p FOR ALL PRIMES p......Page 53
References......Page 56
1 Introduction......Page 58
2 Calculating p(G), c(G) and q(G)......Page 59
3 Quasi-permutation representations of an extraspecial 2-group......Page 61
References......Page 63
1 Introduction......Page 64
2 Preliminaries......Page 65
4 Families of M-groups......Page 67
5 Relations between Hurwitz, H, and M-groups......Page 70
References......Page 71
1 Introduction......Page 73
2 The proof of the Theorem......Page 74
3 Final remarks......Page 75
References......Page 76
1 Introduction......Page 77
2.1 Computational algorithms......Page 78
2.2 Low index subgroups......Page 79
2.3 Low index normal subgroups......Page 80
2.4 Schreier coset graphs......Page 81
3.1 Hurwitz’s theorem......Page 84
3.2 Hurwitz groups......Page 85
4.1 Definitions and background......Page 87
4.2 Genus calculation......Page 89
4.3 Group theoretic construction of regular maps......Page 90
4.4 Non-orientable regular maps......Page 91
4.5 Regular maps of small genus......Page 92
4.6 Group actions on non-orientable surfaces......Page 93
5.1 Definitions and background......Page 96
5.2 The trivalent case......Page 99
5.3 Finite 7-arc-transitive graphs......Page 100
7 Some open problems......Page 102
References......Page 103
1 Introduction......Page 106
2 Relevant families of subgroups being F-dual pronormal......Page 107
3 Local normality concepts between Fitting classes......Page 112
References......Page 114
1 Introduction......Page 115
2 (p, q, r)-Generations for O’N......Page 116
References......Page 122
2 Investigating almost crystallographic groups......Page 124
2.2 Polycyclically presented almost crystallographic groups......Page 125
3 Constructing almost crystallographic groups......Page 127
3.1 Constructing almost Bieberbach groups......Page 130
3.2 An example application......Page 131
4 Further applications......Page 132
References......Page 133
Introduction......Page 134
Who cares about this stuff?......Page 136
1 Random walk and representation theory......Page 137
2 Analytic geometry......Page 143
3 Other appearances of random transpositions......Page 147
4 Some open problems......Page 151
References......Page 153
1 Survey of results......Page 157
2 Inequalities and examples......Page 160
3 Computations......Page 161
References......Page 163
1.1 Euler......Page 164
1.3 Dedekind......Page 166
1.4 Artin, Hasse, Weil......Page 167
1.5 Birch Swinnerton-Dyer......Page 168
1.6 Borevich, Shafarevich, and Igusa......Page 169
1.7 Non-commutative zeta functions......Page 171
2 Using p-adic integrals to capture finite p-groups......Page 172
3 Uniformity......Page 180
4 Subgroup growth and Euler products of cone integrals......Page 190
5.1 Direct products of Heisenberg groups......Page 193
5.2 Zeta functions of Heisenberg groups over number fields......Page 194
5.3 Class two quotients of…......Page 195
5.4 Grenham’s examples......Page 196
5.5 Maximal class nilpotent lie algebras......Page 198
5.6 Free class two three generator group......Page 199
5.7 Functional equations......Page 200
References......Page 202
1 Introduction......Page 204
2 Hypercentrally embedded subgroups......Page 205
3 Factorizations of hypercentrally embedded subgroups with F-normalizers......Page 206
4 Factorizations of hypercentrally embedded subgroups with pre-frattini subgroups......Page 207
5 Final remarks......Page 208
References......Page 210
1 Introduction......Page 211
2 First-order languages and model theory......Page 212
3 The Tarksi problems......Page 217
4 Residually free and universally free groups......Page 220
5 Algebraic geometry over groups and applications......Page 228
6 The positive solution to the Tarski problems......Page 232
7 Discriminating, co-discriminating and squarelike groups......Page 238
References......Page 243
1 Introduction......Page 246
3 Some PEACE proofs and their proof words......Page 247
4 A diffcult example......Page 249
References......Page 250
1 Introduction......Page 252
2 Technique......Page 253
3 Results......Page 254
4 Conclusions......Page 256
References......Page 257
2 Some history of the problem......Page 258
3 Idea of the proof and accompanying results......Page 259
References......Page 261
1 Introduction......Page 263
2 Groups with small finite lengths......Page 264
3 Elements of finite length......Page 267
4 Groups with all elements of finite length......Page 268
References......Page 269
1 Introduction......Page 270
2.2 From group presentations to identities among relators......Page 272
2.3 Logged rewriting and logged Knuth-Bendix completion......Page 274
2.4 Example of logged rewriting......Page 276
3 Resolvingcritical pairs and computing identities among relators......Page 277
4 Computing a crossed resolution......Page 282
5 Examples......Page 284
References......Page 289
1 Introduction......Page 291
2 Preliminary results......Page 292
3 Proof of the main theorem......Page 294
References......Page 297
2 Preliminaries......Page 298
3 Rings with periodic associated group......Page 300
4 Associated groups with finite conjugacy classes......Page 302
5 Rings with nilpotent associated groups......Page 303
6 On semiperfect rings satisfying the Engel condition......Page 305
References......Page 306