@article{PMIHES_2003__96__43_0,
author = {Ol{\textquoteright}shanskii, Alexander Yu. and Sapir, Mark V.},
title = {Non-amenable finitely presented torsion-by-cyclic groups},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {43--169},
year = {2003},
publisher = {Institut des Hautes Etudes Scientifiques},
volume = {96},
zbl = {1050.20019},
language = {en},
url = {https://www.numdam.org/item/PMIHES_2003__96__43_0/}
}
TY - JOUR AU - Ol’shanskii, Alexander Yu. AU - Sapir, Mark V. TI - Non-amenable finitely presented torsion-by-cyclic groups JO - Publications Mathématiques de l'IHÉS PY - 2003 SP - 43 EP - 169 VL - 96 PB - Institut des Hautes Etudes Scientifiques UR - https://www.numdam.org/item/PMIHES_2003__96__43_0/ LA - en ID - PMIHES_2003__96__43_0 ER -
%0 Journal Article %A Ol’shanskii, Alexander Yu. %A Sapir, Mark V. %T Non-amenable finitely presented torsion-by-cyclic groups %J Publications Mathématiques de l'IHÉS %D 2003 %P 43-169 %V 96 %I Institut des Hautes Etudes Scientifiques %U https://www.numdam.org/item/PMIHES_2003__96__43_0/ %G en %F PMIHES_2003__96__43_0
Ol’shanskii, Alexander Yu.; Sapir, Mark V. Non-amenable finitely presented torsion-by-cyclic groups. Publications Mathématiques de l'IHÉS, Tome 96 (2003), pp. 43-169. https://www.numdam.org/item/PMIHES_2003__96__43_0/
[1] , Random walks on free periodic groups, Izv. Akad. Nauk SSSR, Ser. Mat., 46(6) (1982), 1139-1149. | Zbl | MR
[2] , The Burnside problem and identities in groups, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], 95, 311 pp. Berlin-New York: Springer, 1979. | Zbl | MR
[3] , Periodic products of groups. Number theory, mathematical analysis and their applications, Trudy Math Inst. Steklov, 142 (1976), 3-21, 268. | Zbl | MR
[4] and , Sur la décomposition de ensembles de points an parties respectivement congruentes. Fund. math., 6 (1924), 244-277. | JFM
[5] , , and , Isoperimetric functions of groups and computational complexity of the word problem, Ann. Math., 156(2) (2002), 467-518. | Zbl
[6] and , Groups of piecewise linear homeomorphisms of the real line, Invent. Math., 79(3) (1985), 485-498. | Zbl | MR
[7] , and , Introductory notes on Richard Thompson's groups. L'Enseignement Mathématique (2), 42(3-4) (1996), 215-256. | Zbl
[8] and , The algebraic theory of semigroups, Vol. I, Mathematical Surveys, No. 7, Providence, R.I.: American Mathematical Society, 1961. | Zbl | MR
[9] , Cogrowth and amenability of discrete groups, J. Funct. Anal., 48(3) (1982), 301-309. | Zbl | MR
[10] , Amenable semigroups, Illinois J. Math., 1 (1957), 509-544. | Zbl | MR
[11] , On groups with full Banach mean value, Math. Scand., 3 (1955), 243-254. | Zbl | MR
[12] Open problems in infinite-dimensional topology, ed. by , The Proceedings of the 1979 Topology Conference (Ohio Univ., Athens, Ohio, 1979), Topology Proc., 4(1) (1979), 287-338 (1980). | Zbl | MR
[13] , Invariant means on topological groups and their applications, New York: Van Nostrand Reinhold, 1969. | Zbl | MR
[14] , Symmetrical random walks on discrete groups, Multicomponent random systems, Adv. Probab. Related Topics, 6 (1980), 285-325, New York: Dekker | Zbl | MR
[15] , An example of a finitely presented amenable group that does not belong to the class EG, Mat. Sb., 189(1) (1998), 79-100. | Zbl | MR
[16] , Grundzüge der Mengenlehre, Leipzig, 1914. | JFM
[17] , On HNN-extensions in the class of groups of a large odd exponent, Preprint, 2002. | Zbl
[18] and , Hyperbolic groups and their quotients of bounded exponents, Trans. Amer. Math. Soc., 348(6) (1996), 2091-2138. | Zbl
[19] , Full Banach mean values on countable groups, Math. Scand., 7 (1959), 146-156. | Zbl | MR
[20] , Symmetric random walks on groups, Trans. Amer. Math. Soc., 92 (1959), 336-354. | Zbl | MR
[21] and , Algorithmic problems in varieties, Internat. J. Algebra Comput., 5(4-5) (1995), 379-602. | Zbl | MR
[22] Kourovka Notebook, Unsolved Problems in Group Theory, 8th edition, Novosibirsk, 1982.
[23] and , Combinatorial group theory, Springer, 1977. | Zbl | MR
[24] K. V. MIKHAJLOVSKII, Some generalizations of the HNN-construction in the periodic case, #1063-B94, VINITI, Moscow, 1994, 59 pp.
[25] , Zur allgemeinen Theorie des Masses, Fund. math., 13 (1929), 73-116. | JFM
[26] P. S. NOVIKOV and S. I. ADIAN, Infinite periodic groups, I, II, III (Russian), Izv. Akad. Nauk SSSR Ser. Mat., 32 (1968), 212-244, 251-524, 709-731. | Zbl | MR
[27] , An infinite simple torsion-free Noetherian group, Izv. Akad. Nauk SSSR Ser. Mat., 43(6) (1979), 1328-1393. | Zbl
[28] , An infinite group with subgroups of prime order, Izvestia Akad. Nauk SSSR, Ser. Mat., 44(2) (1980), 309-321. | Zbl
[29] , On the question of the existence of an invariant mean on a group (Russian), Uspekhi Mat. Nauk, 35(4(214)) (1980), 199-200. | Zbl
[30] , The geometry of defining relations in groups, Moscow: Nauka, 1989. | Zbl
[31] , The SQ-universality of hyperbolic groups, Mat. Sb., 186(8) (1995), 119-132. | Zbl
[32] , On distortion of subgroups in finitely presented groups, Mat. Sb., 188(11) (1997), 51-98. | Zbl
[33] and , Embeddings of relatively free groups into finitely presented groups, Contemp. Math., 264 (2000), 23-47. | Zbl
[34] and , Length and Area Functions on Groups and Quasi-Isometric Higman Embeddings, J. Algebra and Comp., 11(2) (2001), 137-170. | Zbl
[35] , Problems of Burnside type and the finite basis property in varieties of semigroups, Izv. Akad. Nauk. SSSR., Ser. Mat., 51(2) (1987), 319-340. | Zbl | MR
[36] , and , Isoperimetric and isodiametric functions of groups, 1997, Ann. Math., 156(2) (2002), 345-466. | Zbl | MR
[37] , Zur Theorie der messbaren Gruppen, Math. Z., 74 (1960), 325-366. | Zbl | MR
[38] , Free subgroups of linear groups, J. Algebra, (20) (1972), 250-270. | Zbl | MR
[39] A. M. VERSHIK, Comments to papers by J. von Neumann, in “J. von Neumann, Selected works in functional analysis”, Moscow: Nauka, v1 (1987), 357-376.
