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## Colloquium Mathematicum

1999 | 82 | 1 | 1-12
Tytuł artykułu

### Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
1-12
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-12-03
poprawiono
1999-03-10
Twórcy
autor
• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
• [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.
• [2] C. Alperin and H. Bass, Length functions of groups actions on $\mitΛ$-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.
• [3] V. V. Belyaev, Locally finite groups with a finite non-separable subgroup, Sibirsk. Mat. Zh. 34 (1993), 23-41 (in Russian).
• [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.
• [5] H. Furstenberg, Poincaré recurrence and number theory, Bull. Amer. Math. Soc. 5 (1981), 211-234.
• [6] Yu. Gorchakov, Groups with Finite Conjugacy Classes, Nauka, Moscow, 1978 (in Russian).
• [7] Yu. Gorchinskiĭ, Periodic groups with a finite number of conjugacy classes, Mat. Sb. 31 (1952), 209-216 (in Russian).
• [8] R. Grigorchuk, An example of a finitely presented amenable group not belonging to the class $EG$, ibid. 189 (1998), 79-100 (in Russian).
• [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)).
• [10] M. Kargapolov and Yu. Merzlyakov, Basic Group Theory, Nauka, Moscow, 1977 (in Russian).
• [11] P. Longobardi, M. Maj and A. H. Rhemtulla, Groups with no free subsemigroups, Proc. Amer. Math. Soc., to appear.
• [12] Yu. I. Merzlyakov, Rational Groups, Nauka, Moscow, 1980 (in Russian).
• [13] A. Yu. Olshanskiĭ, Geometry of Defining Relations in Groups, Nauka, Moscow, 1989 (in Russian).
• [14] J.-P. Serre, Trees, Springer, New York, 1980.
• [15] V. P. Shunkov, On periodic groups with almost regular involutions, Algebra i Logika 11 (1972), 470-493 (in Russian).
• [16] A. I. Sozutov, On groups with Frobenius pairs, ibid. 16 (1977), 204-212 (in Russian).
• [17] A. I. Sozutov and V. P. Shunkov, On infinite groups with Frobenius subgroups, ibid. 16 (1977), 711-735 (in Russian).
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Bibliografia
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