We study infinite finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups. The results concern growth and the ascending chain condition for such groups.
@article{bwmeta1.element.bwnjournal-article-cmv82i1p1bwm, author = {A. Ivanov}, title = {Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups}, journal = {Colloquium Mathematicae}, volume = {79}, year = {1999}, pages = {1-12}, zbl = {0945.20026}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p1bwm} }
Ivanov, A. Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups. Colloquium Mathematicae, Tome 79 (1999) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p1bwm/
[000] [1] I. Aguzarov, R. E. Farey and J. B. Goode, An infinite superstable group has infinitely many conjugacy classes, J. Symbolic Logic 56 (1991), 618-623. | Zbl 0743.03024
[001] [2] C. Alperin and H. Bass, Length functions of groups actions on -trees, in: Combinatorial Group Theory and Topology, S. M. Gersten and J. R. Stallings (eds.), Ann. of Math. Stud. 111, Princeton Univ. Press, 1987, 265-378.
[002] [3] V. V. Belyaev, Locally finite groups with a finite non-separable subgroup, Sibirsk. Mat. Zh. 34 (1993), 23-41 (in Russian).
[003] [4] T. Ceccherini-Silberstein, R. Grigorchuk and P. de la Harpe, Amenability and paradoxes for pseudogroups and for metric spaces, preprint, Geneve 1997, 33 pp. | Zbl 0968.43002
[004] [5] H. Furstenberg, Poincaré recurrence and number theory, Bull. Amer. Math. Soc. 5 (1981), 211-234. | Zbl 0481.28013
[005] [6] Yu. Gorchakov, Groups with Finite Conjugacy Classes, Nauka, Moscow, 1978 (in Russian).
[006] [7] Yu. Gorchinskiĭ, Periodic groups with a finite number of conjugacy classes, Mat. Sb. 31 (1952), 209-216 (in Russian).
[007] [8] R. Grigorchuk, An example of a finitely presented amenable group not belonging to the class , ibid. 189 (1998), 79-100 (in Russian). | Zbl 0931.43003
[008] [9] A. Ivanov, The problem of finite axiomatizability for strongly minimal theories of graphs, Algebra and Logic 28 (1989), 183-194 (English translation from Algebra i Logika 28 (1989)). | Zbl 0727.05028
[009] [10] M. Kargapolov and Yu. Merzlyakov, Basic Group Theory, Nauka, Moscow, 1977 (in Russian). | Zbl 0499.20001
[010] [11] P. Longobardi, M. Maj and A. H. Rhemtulla, Groups with no free subsemigroups, Proc. Amer. Math. Soc., to appear. | Zbl 0833.20043
[011] [12] Yu. I. Merzlyakov, Rational Groups, Nauka, Moscow, 1980 (in Russian).
[012] [13] A. Yu. Olshanskiĭ, Geometry of Defining Relations in Groups, Nauka, Moscow, 1989 (in Russian).
[013] [14] J.-P. Serre, Trees, Springer, New York, 1980.
[014] [15] V. P. Shunkov, On periodic groups with almost regular involutions, Algebra i Logika 11 (1972), 470-493 (in Russian).
[015] [16] A. I. Sozutov, On groups with Frobenius pairs, ibid. 16 (1977), 204-212 (in Russian).
[016] [17] A. I. Sozutov and V. P. Shunkov, On infinite groups with Frobenius subgroups, ibid. 16 (1977), 711-735 (in Russian). | Zbl 0405.20040