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| Fine B., Rosenberger G. — Algebraic Generalizations of Discrete Groups: A Path to Combinatorial Group Theory Through One-Relator Products |
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| Предметный указатель |
A-thin triangles 27
Aab, M. 56 64 20
Adjunction problem 112—113
Allenby, R. 56 98 239 240 241
Alperin, R. 32 34 60 66 96
Amalgamated free product 11
Anshel, I. 49
Arboreal group theory 31—34
Asynchronous automatic structure 37
Automatic groups 34—38
Automatic structure 36 37
Bagherzadeh, G.H. 76 120
Base of an HNN group 13
Bass — Serre theory 16—18
Bass, H. 17 32 34 52 60 66 67 98 214 216 237 286 287
Baumslag — Shalen decomposition 58
Baumslag — Solitar group 64
Baumslag, B. 50 66 67 114 140 173 260 276
Baumslag, G. 4 37 39 46 49 54 55 56 58 62 75 138 140 145 147 171 203 228 249
Beardon, A. 79 80
Bencsath, K. 75
Bestvina, M. 30 58 251
Biautomatic group 37
Bieri, R. 58
Bogley, W. 47 49
Boyer, S. 147
Britton, W. 71
Brodskii, S.D. 53 114 117 121
Brown, K. 97 216 217 237 238
Brunner, A. 56 64 239
Burns, R. 56 64 239
Cannon, J. 34 35
Chandler, B. 62
Character variety 212
Chiswell, I. 31 32 33 34 67 98 154 216 237
Cocompact Fuchsian group 88
Cohen — Lyndon theorem 120
Cohen, D.E. 120
Cohen, M. 30
Coldeway, H. 104
Collins, D. 19 21 124 126 210 211
Commutative transitive 46
Conder, M. 171 203 221
Confluence 36
Conjecture F 128
Conjugacy pinched one relator groups 59—64
Conjugacy problem 26
Conjugacy separable 56
Context-free group 36
Context-free language 35
Corson, J. 126
Coxeter, H.S.M. 253 267 289
Culler, M. 4 51 160 212
Cyclically pinched one relator groups 53—59
Cyclically reduced in a free group 6
Cyclically reduced in a free product 12
Decidable theory 65
Deficiency 50
Dehn algorithm 27 28
Dehn, M. 26 27 46 70
Delta-thin triangles 28
Dicks, W. 6
Dirichlet region 88
Discontinuous group 80
Discrete groups 110—177
Duncan, A. 112 118 128 131 211 217
Dunwoody 213
Dyer, J. 56 98 241
Eckmann, B. 76
Edjvet, M. 117 120 164 260 289
Elementarily equivalent 66
Elementarily free group 66
Elementary embedding 65
Elementary Nielsen transformation 19
Elementary subgroup 81
Elementary theory 65
Elliptic transformation 78
Epstein, D.B.A. 34
Equations over groups 112—113
Essential representation 139
Essentially faithful representation 139
Euler characteristic for Fuchsian groups 2 90
Euler characteristic for generalized tetrahedron groups 288
Euler characteristic for groups of F-type 237
Euler characteristic for one-relator products 216—220
Extended deficiency 139
Extension of centralizers 68
F-group 2 91 222
Factor in a free product 9
Factor in a one-relator product 1
Feign, M. 30 58 251
Fenchel — Fox theorem 96
Fenchel, W. 51
FHS see "Freiheitssatz"
Fine, B. 19 25 30 55 56 58 60 61 62 66 68 75 98 106 203 238 249
Finite generalized tetrahedron groups 289—290
Finite generalized triangle groups 201—208
Finite state automaton 35
Fischer, J. 51 140 208
Fixed point 78
Ford domain 83
Fox, R. 51 96
Free actions 17
Free exponential group 68
Free group 6
Free group rank 6
Free length 6
Free product 9
Free product with amalgamation 11
Freely reduced word 6
Freiheitssatz (FHS) factor 41
Freiheitssatz (FHS) for generalized tetrahedron groups 284
Freiheitssatz (FHS) for groups of F-type 226
Freiheitssatz (FHS) for groups of SN-type 255
Freiheitssatz (FHS) for one-relator amalgamated products 149—152
Freiheitssatz (FHS) for one-relator products of cyclic groups 144—148
Freiheitssatz (FHS) for one-relator products, high-powered relators 121—130
Freiheitssatz (FHS) for one-relator products, locally indicable factors 113—117
Freiheitssatz (FHS) for small cancellation products 125
Freiheitssatz (FHS), general 40
Fuchsian groups 81—103
Fuchsian groups, algebraic analysis 89—103
Fuchsian representation 169
Fully residually free 66
Fundamental domain, Fuchsian groups 82
Fundamental domain, groups acting on trees 17
Gaglione, A. 25 55 56 66 67 68
Generalized tetrahedron groups 266—290
Generalized triangle group factor 268
Generalized triangle groups 166—220
Generalized word problem 248
Genus 90
Genus problems 118
Geometric group theory 25—38
Geometric rank 106
Gersten conjecture 31
Gersten — Stallings angle 284
Gersten, S. 31 37 132 269 284
Gerstenhaber, M. 132
Gilman, J. 107
Gitik, R. 64
Gonzalez-Acuna, F. 112 126
Greendlinger, M. 71 72
Gromov, M. 25 27 28 29 45 58
Group amalgam 11
Groups of F-type 221—252
Groups of SN-type 254—266
Groups of special NEC-type 254—266
Gurevich, G.A. 118
Hagelberg, M. 153
| Harrison, N. 34
Helling, H. 4 51 153
Hempel, A. 229
Higman, G. 14 96 113 140 171
HNN extension 13
HNN group 13
Hoare, A.H. 76 97 98 104
Holt, D. 34
Howie's tower proof 48
Howie, J. 3 46 47 48 53 112 114 117 118 120 121 128 131 132 160 175 189 193 202 203 208 210 211 217
Hurwitz groups 171
Hyperbolic groups 25—31
Hyperbolic transformation 78
Isomorphism problem 26
Johnson, D. 7
Juhasz, A. 30 45 57 58 124 248 151
Kalia, R.N. 19 21
Karrass, A. 6 15 16 49 51 76 97 98 104 140 208 251 268
Katok, S. 79
Kaufmann 106 253 264 266
Kerckhoff, S.P. 76
Kervaire conjecture 113 130—136
Kervairs, M. 113 131
Kharlamapovich, O. 30 58 66 67 69 251
Kim, A. 153
Kim, G. 56 63 64
Klyachko's theorem 131
Klyachko, A. 113 121 131
Klymenko, E. 109
Kurosh theorem 10
Lambda-free group 34
Lambda-tree 33
Lerf 56
Levai, L. 160 202 203
Levin, F. 67 96 113 132 163 192 203
Limit points 80 237
Linear fractional transformation 77
Linear isoperimetric inequality 28
Linear properties, groups of F-type 231—248
Linear properties, groups of SN-type 258—266
Linear properties, tetrahedron groups 274—289
Lipschutz, S. 57 248
Liriano, S. 62
Litz, S. 152
Locally indicable 53 113—117
Long, D. 213
Loop 18
Lossov, K.I. 191
Loxodromic transformation 78
LRS monster 202
Lustig, M. 30 285
Lyndon length function 33
Lyndon Van-Kampen diagram 72
Lyndon's Identity theorem 119
Lyndon, R. 6 39 40 49 71 72 73 97 114 119 131 222
Lysenok, I.G. 27 28
Macalachlan, C. 152 213
MacBeath, M. 104 171
Magnus method 42
Magnus relators 250
Magnus subgroups 76
Magnus, W. 6 39 40 41 42 43 49 62 70 74 114 118 119 155 168 248 251
Mahmud, R.M.S. 126
Majeed, A. 109 162 198
Malcev, A.I. 232
Martinez, E. 104
Maskit, B. 87 107
Maximum Modulus Principle 73
McCool, J. 41 114
Mendelsohn, N.S. 4 50 144
Mennicke, J. 153
Metafsis, V. 160 202 203 208
Moebius transformation 77
Moldavanskii, D.I. 41 114
Morgan, J. 4 31 32 138 140 145 147 203
Muller, D.E. 36 76 171
Multipier 78
Murasugi, K. 46 75
Myasnikov, A. 30 58 66 67 68 69 251
n-free 54
NEC groups 103—110
Neumann, B.H. 14 131 221
Neumann, H. 14 140
Neumann, RM. 96
Newman, B.B. 45 51 117 140 248
Niblo, G. 56 63 64 239 240
Nielsen equivalence 19
Nielsen Realization Problem 76
Nielsen reduction 20—23
Nielsen transformation 18—25
Nielsen — Schreier theorem 7
Nielsen, J. 96
Non-Euclidean crystallographic group 103—110
Normal form in a free group 6
Normal form in a free product 10
Normal form in an amalgamated free product 11
Normal form in an HNN group 13
Olshanskii, Y. 124
One-relator amalgamated products 149
One-relator groups 1 39—76
One-relator products 1 111—136
One-relator products of cyclics 2 137—220
One-relator products, linear properties 159—220
One-relator products, Tits alternative 160—166
Ordinary tetrahedron groups 267
Ordinary triangle groups 91 167—171
Papakyriapopolous towers 46
Parabolic transformation 78
Parafree group 62
Patterson, M.S. 34
Peczynski, N. 19 23 25 60 106
Peluso, A. 58
Perraud, F. 124 126 210 211
Pictures over groups 126
Pietrowski, A. 268
Poincare polygon 87
Poincare presentation 2 89
Polygonal product 268
Power conjugacy problem 248
Pride, S. 45 47 49 50 114 117 118 140 173 249 260 276 284
Purzitsky, N. 106
Quasiconvex 29
R-diagram 73
R-free group 32
R-tree 32
Ratcliffe, J. 154
Reduced sequence, free product 10
Reduced sequence, free product with amalgamation 11
Ree — Mendelsohn pairs 167 194
Ree — Mendelsohn theorem 50
Ree, R. 50 144
Regular language 35
Reid, A. 213
Reiwer, W. 19 23 25 60
Remeslennikov, V. 66 67 69
Residually finite 56
Residually free 66
Restricted Gromov (RG) group 30
Rewriting rule 25
Riemann — Hurwitz formula, Fuchsian groups 97
Riemann — Hurwitz formula, groups of F-type 237
Riemann — Hurwitz formula, one-relator products 217
Rips complex 31
Rips theorem 32
Rips, E. 31 32 124
RM-pairs 167
Rohl, F. 25 60 61
Rosenberger, G. 4 19 21 23 25 55 56 60 61 62 63 66 67 68 98 106 153 160 192 202 203 228 230 238 249 251 269 289
Rothaus, O. 132
Rourke, C.P. 126
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