Non-amenable finitely presented torsion-by-cyclic groups

 Access to full text

 Full (PDF)

1. [1] S. I. ADIAN, Random walks on free periodic groups, Izv. Akad. Nauk SSSR, Ser. Mat., 46(6) (1982), 1139-1149. Zbl0512.60012MR682486
2. [2] S. I. ADIAN, 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. Zbl0417.20001MR537580
3. [3] S. I. ADIAN, Periodic products of groups. Number theory, mathematical analysis and their applications, Trudy Math Inst. Steklov, 142 (1976), 3-21, 268. Zbl0424.20020MR532668
4. [4] S. BANACH and A. TARSKI, Sur la décomposition de ensembles de points an parties respectivement congruentes. Fund. math., 6 (1924), 244-277. Zbl50.0370.02JFM50.0370.02
5. [5] J. C. BIRGET, A. Yu. OL’SHANSKII, E. RIPS and M. V. SAPIR, Isoperimetric functions of groups and computational complexity of the word problem, Ann. Math., 156(2) (2002), 467-518. Zbl1026.20018
6. [6] M. G. BRIN and C. C. SQUIER, Groups of piecewise linear homeomorphisms of the real line, Invent. Math., 79(3) (1985), 485-498. Zbl0563.57022MR782231
7. [7] J. W. CANNON, W. J. FLOYD and W. R. PARRY, Introductory notes on Richard Thompson’s groups. L’Enseignement Mathématique (2), 42(3-4) (1996), 215-256. Zbl0880.20027
8. [8] A. H. CLIFFORD and G. B. PRESTON, The algebraic theory of semigroups, Vol. I, Mathematical Surveys, No. 7, Providence, R.I.: American Mathematical Society, 1961. Zbl0111.03403MR132791
9. [9] J. M. COHEN, Cogrowth and amenability of discrete groups, J. Funct. Anal., 48(3) (1982), 301-309. Zbl0499.20023MR678175
10. [10] M. M. DAY, Amenable semigroups, Illinois J. Math., 1 (1957), 509-544. Zbl0078.29402MR92128
11. [11] E. FØLNER, On groups with full Banach mean value, Math. Scand., 3 (1955), 243-254. Zbl0067.01203MR79220
12. [12] Open problems in infinite-dimensional topology, ed. by Ross Geoghegan, The Proceedings of the 1979 Topology Conference (Ohio Univ., Athens, Ohio, 1979), Topology Proc., 4(1) (1979), 287-338 (1980). Zbl0448.57001MR583711
13. [13] F. P. GREENLEAF, Invariant means on topological groups and their applications, New York: Van Nostrand Reinhold, 1969. Zbl0174.19001MR251549
14. [14] R. I. GRIGORCHUK, Symmetrical random walks on discrete groups, Multicomponent random systems, Adv. Probab. Related Topics, 6 (1980), 285-325, New York: Dekker Zbl0475.60007MR599539
15. [15] R. I. GRIGORCHUK, An example of a finitely presented amenable group that does not belong to the class EG, Mat. Sb., 189(1) (1998), 79-100. Zbl0931.43003MR1616436
16. [16] F. HAUSDORFF, Grundzüge der Mengenlehre, Leipzig, 1914. JFM45.0123.01
17. [17] S. V. IVANOV, On HNN-extensions in the class of groups of a large odd exponent, Preprint, 2002. Zbl1042.20024
18. [18] S. V. IVANOV and A. Y. OL’SHANSKII, Hyperbolic groups and their quotients of bounded exponents, Trans. Amer. Math. Soc., 348(6) (1996), 2091-2138. Zbl0876.20023
19. [19] H. KESTEN, Full Banach mean values on countable groups, Math. Scand., 7 (1959), 146-156. Zbl0092.26704MR112053
20. [20] H. KESTEN, Symmetric random walks on groups, Trans. Amer. Math. Soc., 92 (1959), 336-354. Zbl0092.33503MR109367
21. [21] O. G. KHARLAMPOVICH and M. V. SAPIR, Algorithmic problems in varieties, Internat. J. Algebra Comput., 5(4-5) (1995), 379-602. Zbl0837.08002MR1361261
22. [22] Kourovka Notebook, Unsolved Problems in Group Theory, 8th edition, Novosibirsk, 1982. 
23. [23] R. LYNDON and P. SCHUPP, Combinatorial group theory, Springer, 1977. Zbl0997.20037MR577064
24. [24] K. V. MIKHAJLOVSKII, Some generalizations of the HNN-construction in the periodic case, #1063-B94, VINITI, Moscow, 1994, 59 pp. 
25. [25] J. VON NEUMANN, Zur allgemeinen Theorie des Masses, Fund. math., 13 (1929), 73-116. JFM55.0151.01
26. [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. Zbl0194.03301MR240178
27. [27] A. Yu. OL’SHANSKII, An infinite simple torsion-free Noetherian group, Izv. Akad. Nauk SSSR Ser. Mat., 43(6) (1979), 1328-1393. Zbl0431.20027
28. [28] A. Yu. OL’SHANSKII, An infinite group with subgroups of prime order, Izvestia Akad. Nauk SSSR, Ser. Mat., 44(2) (1980), 309-321. Zbl0475.20025
29. [29] A. Yu. OL’SHANSKII, On the question of the existence of an invariant mean on a group (Russian), Uspekhi Mat. Nauk, 35(4(214)) (1980), 199-200. Zbl0452.20032
30. [30] A. Yu. OL’SHANSKII, The geometry of defining relations in groups, Moscow: Nauka, 1989. Zbl0676.20014
31. [31] A. Yu. OL’SHANSKII, The SQ-universality of hyperbolic groups, Mat. Sb., 186(8) (1995), 119-132. Zbl0864.20023
32. [32] A. Yu. OL’SHANSKII, On distortion of subgroups in finitely presented groups, Mat. Sb., 188(11) (1997), 51-98. Zbl0905.20020
33. [33] A. Yu. OL’SHANSKII and M. V. SAPIR, Embeddings of relatively free groups into finitely presented groups, Contemp. Math., 264 (2000), 23-47. Zbl0987.20015
34. [34] A. Yu. OL’SHANSKII and M. V. SAPIR, Length and Area Functions on Groups and Quasi-Isometric Higman Embeddings, J. Algebra and Comp., 11(2) (2001), 137-170. Zbl1025.20030
35. [35] M. V. SAPIR, Problems of Burnside type and the finite basis property in varieties of semigroups, Izv. Akad. Nauk. SSSR., Ser. Mat., 51(2) (1987), 319-340. Zbl0646.20047MR897000
36. [36] M. V. Sapir, J. C. BIRGET and E. RIPS, Isoperimetric and isodiametric functions of groups, 1997, Ann. Math., 156(2) (2002), 345-466. Zbl1026.20021MR1933723
37. [37] W. SPECHT, Zur Theorie der messbaren Gruppen, Math. Z., 74 (1960), 325-366. Zbl0093.24603MR140641
38. [38] J. TITS, Free subgroups of linear groups, J. Algebra, (20) (1972), 250-270. Zbl0236.20032MR286898
39. [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.