Aspects of Infinite Groups: A Festschrift in Honor of Anthony Gaglione

CONTENTS......Page 8
Preface......Page 6
1. Introduction......Page 10
2. The Algebraic Eraser™ and its Key Agreement Protocol:......Page 11
3. Related Algebraic Constructions......Page 13
4. References......Page 17
1. Introduction......Page 18
2. The groups Gn......Page 19
3. The method of Reidemeister and Schreier......Page 20
4. The surface property......Page 22
5.1. The relators p(b-l[a, b]nbl ).......Page 23
5.1.1. The case when C is even......Page 24
5.1.2. The case when £ is odd......Page 25
5.2. The relators p(b-la-1 [a, b]nabl )......Page 26
5.3. Parametric form for the kernel of ¢......Page 28
6. The kernel K of 1j; : H ---t (z ; ) is free......Page 30
7. Computational support......Page 33
8. Virtually locally free by cyclic groups......Page 32
References......Page 34
Some Cryptoprimitives for Noncommutative Algebraic Cryptography G. Baumslag, Y. Bryukhov, B. Fine and G. Rosenberger......Page 35
1. Introduction......Page 36
2. The Basics of Free Group Cryptography......Page 38
3. A General Schema for Nonabelian Group Diffie-Hellman......Page 39
4. Polyalphabetic Free Group Cryptosystems......Page 41
5. Factoring in Noncommutative Rings......Page 44
6. Formal Power Series Rings and the Magnus Representation......Page 46
8. References......Page 52
1. Introduction......Page 54
2. The Derived Subgroup of a Free Nilpotent Group......Page 56
3. Application......Page 61
References......Page 62
A Recurrence Relation for the Number of Free Subgroups in Free Products of Cyclic Groups T. Camps, M. Darfer and G. Rosenberger......Page 63
1. Introduction......Page 64
2. Preliminaries......Page 65
3. The Main Results......Page 77
4. Examples......Page 81
References......Page 82
2. Notation......Page 84
3. The proof of Theorem 1.1......Page 85
References......Page 88
CONTENTS......Page 89
1. Introduction......Page 90
2.1. Languages and structures......Page 91
2.2. Theories......Page 93
3. Algebras......Page 94
3.1. Congruences......Page 95
3.2. Quasivarieties......Page 96
3.3. Universal closures......Page 100
3.4. A-Algebras......Page 103
4.1. Quantifier-free types and Zariski topology......Page 105
4.2. Coordinate algebras and complete types......Page 107
4.3. Equationally Noetherian algebras......Page 109
5.1. Direct systems of formulas and limit algebras......Page 111
5.2. Limit A-algebras......Page 115
6. Unification Theorems......Page 116
References......Page 117
1. Introduction......Page 121
2. Commutative Transitivity and Commutative Transitive Groups......Page 123
3. Commutative Transitivity, CSA and Universally Free Groups......Page 126
4. The Commutative Transitive Kernel......Page 130
5. RG Groups and a Classification of One-Relator CT Groups......Page 133
6. Commutative Transitivity and Discriminating Groups......Page 134
7. An Extension of Commutative Thansitivity......Page 135
8. References......Page 137
1. Introduction......Page 140
2. Preliminaries......Page 142
3. Varieties and Discrimination......Page 144
4. The Variety 0 of All Groups......Page 146
5. The Burnside Varieties......Page 151
6. A Possible Non-Free Model and a Question of Philip Hall......Page 153
8. References......Page 155
Main Theorem......Page 158
References......Page 159
1. Introduction......Page 160
2. Results......Page 161
References......Page 167
1. Introduction......Page 168
2. Differential groups......Page 170
2.1. Definitions......Page 171
2.2. Properties......Page 172
2.3. Homology and cohomology......Page 175
3.1. Definitions......Page 176
3.2.1. Bar resolution......Page 179
3.2.3. Homogeneous resolution......Page 183
4. Definition of Hn(G, A)......Page 184
4.1.1. Computer computations of cohomology......Page 185
5. Definition of Hn(G, A)......Page 186
5.1.1. Computer computations of homology......Page 188
5.1.2. Examples......Page 189
6. Basic properties of Hn(G, A), Hn(G, A)......Page 191
7. Functorial properties......Page 196
7.1. Restriction......Page 198
7.2. Inflation......Page 199
References......Page 200
1. Introduction and Motivation......Page 201
2.1. Subgroups of amalgamated products......Page 203
2.2. Some Lemmas......Page 204
2.3. The filtration approach to residual solvability......Page 205
3.2. Effect of solvably separability on the amalgamated subgroup and residual solvability, Proof of Theorem 1.1......Page 206
References......Page 208
1. Introduction......Page 210
3. Conditions on Maximal Abelian Subgroups and the Counterexample......Page 211
4. Property R......Page 214
5. Weak Property R......Page 218
7. References......Page 220
1. Introduction......Page 221
2. Preliminaries......Page 222
3. Elementary Quotient Operations......Page 224
4. The Binary Isomorphism Invariant......Page 225
5. Matching Theorems......Page 227
6. The Even Isomorphism Invariant......Page 228
7. Basic Characteristic Subgroups......Page 231
8. The Spherical Rank Two Invariant......Page 232
9. Conclusion......Page 235
References......Page 236
1. Introduction......Page 237
2. Preliminary discussion......Page 239
3.1. Powers of IA-automorphisms......Page 240
3.2. Proof that I A( G) is p-local if G is p-local......Page 242
3.3. IA(G) -+ IA(G(p» is a p-isomorphism......Page 245
4.1. An example where InnG =I IA(G)......Page 248
4.2. Remeslennikov\'s groups......Page 250
4.3. Pickel-Roitberg groups......Page 251
References......Page 252