Algorithmic and Combinatorial Algebra

L.A. Bokut', G.P.. Kukin

Springer Science & Business Media, May 31, 1994 - Computers - 384 pages

Even three decades ago, the words 'combinatorial algebra' contrasting, for in stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).

Contents

• II: 1
• III: 2
• IV: 5
• V: 17
• VI: 22
• VII: 32
• VIII: 35
• IX: 53
• X: 54
• XI: 55
• XII: 56
• XIII: 57
• XIV: 58
• XV: 60
• XVI: 61
• XVII: 64
• XVIII: 65
• XIX: 66
• XX: 73
• XXI: 74
• XXII: 76
• XXIII: 84
• XXIV: 86
• XXV: 90
• XXVI: 92
• XXVIII: 94
• XXIX: 101
• XXX: 105
• XXXIII: 106
• XXXIV: 111
• XXXV: 118
• XXXVI: 120
• XXXVII: 123
• XXXVIII: 124
• XXXIX: 126
• XL: 127
• XLI: 131
• XLII: 134
• XLIII: 141
• XLIV: 142
• XLV: 143
• XLVII: 144
• XLVIII: 146
• XLIX: 147
• L: 148
• LI: 151
• LII: 152
• LIII: 155
• LIV: 159
• LV: 163
• LVI: 167
• LVII: 171
• LIX: 172
• LX: 174
• LXI: 177
• LXII: 178
• LXIII: 182
• LXIV: 185
• LXV: 188
• LXVI: 197
• LXVII: 199
• LXVIII: 202
• LXIX: 203
• LXX: 206
• LXXI: 209
• LXXVII: 215
• LXXVIII: 218
• LXXIX: 222
• LXXX: 228
• LXXXI: 237
• LXXXII: 240
• LXXXIII: 256
• LXXXIV: 262
• LXXXV: 276
• LXXXVI: 309
• LXXXVII: 315
• LXXXVIII: 323
• LXXXIX: 325
• XC: 327
• XCI: 330
• XCII: 334
• XCIII: 335
• XCIV: 337
• XCVI: 338
• XCVII: 340
• XCVIII: 343
• XCIX: 346
• C: 347
• CI: 349
• CII: 380

Popular passages

Page 366 - Equations in a free group", Izv. Akad. Nauk SSSR, Ser. Mat. 46 (1982) 1199-1273. Transl. in Math. USSR Izv. 21 (1983). [Mak2] GS Makanin, "Decidability of the universal and positive theories of a free group‎

Page 369 - Decision Problems for Groups — Survey and Reflections, Algorithms and Classification in Combinatorial Group Theory (Berkeley, CA, 1989), Math. Sci. Res. Inst. Publ., Springer, New York, 1992, vol. 23, p. 1 - 59. [296] CF Miller III and PE Schupp, 'Embeddings into hopfian groups,‎

Page 355 - An analysis of Turing's 'The word problem in semigroups with cancellation,‎

Bibliographic information

• Title: Algorithmic and Combinatorial Algebra; Mathematics and Its Applications, ISSN 0921-3791
• Authors: L.A. Bokut', G.P.. Kukin
• Edition: illustrated
• Publisher: Springer Science & Business Media, 1994
• ISBN: 0792323130, 9780792323136
• Length: 384 pages
• Subjects: Computers / Programming / Algorithms; Gardening / General; Mathematics / Algebra / General; Mathematics / Applied; Mathematics / Combinatorics; Mathematics / Numerical Analysis