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

A. Ivanov

Colloquium Mathematicae (1999)

  • Volume: 82, Issue: 1, page 1-12
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Ivanov, A.. "Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups." Colloquium Mathematicae 82.1 (1999): 1-12. <http://eudml.org/doc/210748>.

@article{Ivanov1999,
abstract = {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.},
author = {Ivanov, A.},
journal = {Colloquium Mathematicae},
keywords = {finitely generated groups; conjugacy classes; cyclic subgroups; finitely presented groups; threading tuples; groups of subexponential growth; periodic groups; geodesic words},
language = {eng},
number = {1},
pages = {1-12},
title = {Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups},
url = {http://eudml.org/doc/210748},
volume = {82},
year = {1999},
}

TY - JOUR
AU - Ivanov, A.
TI - Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups
JO - Colloquium Mathematicae
PY - 1999
VL - 82
IS - 1
SP - 1
EP - 12
AB - 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.
LA - eng
KW - finitely generated groups; conjugacy classes; cyclic subgroups; finitely presented groups; threading tuples; groups of subexponential growth; periodic groups; geodesic words
UR - http://eudml.org/doc/210748
ER -

References

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  1. [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. Zbl0743.03024
  2. [2] C. Alperin and H. Bass, Length functions of groups actions on Λ -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. [3] V. V. Belyaev, Locally finite groups with a finite non-separable subgroup, Sibirsk. Mat. Zh. 34 (1993), 23-41 (in Russian). 
  4. [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. Zbl0968.43002
  5. [5] H. Furstenberg, Poincaré recurrence and number theory, Bull. Amer. Math. Soc. 5 (1981), 211-234. Zbl0481.28013
  6. [6] Yu. Gorchakov, Groups with Finite Conjugacy Classes, Nauka, Moscow, 1978 (in Russian). 
  7. [7] Yu. Gorchinskiĭ, Periodic groups with a finite number of conjugacy classes, Mat. Sb. 31 (1952), 209-216 (in Russian). 
  8. [8] R. Grigorchuk, An example of a finitely presented amenable group not belonging to the class E G , ibid. 189 (1998), 79-100 (in Russian). Zbl0931.43003
  9. [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)). Zbl0727.05028
  10. [10] M. Kargapolov and Yu. Merzlyakov, Basic Group Theory, Nauka, Moscow, 1977 (in Russian). Zbl0499.20001
  11. [11] P. Longobardi, M. Maj and A. H. Rhemtulla, Groups with no free subsemigroups, Proc. Amer. Math. Soc., to appear. Zbl0833.20043
  12. [12] Yu. I. Merzlyakov, Rational Groups, Nauka, Moscow, 1980 (in Russian). 
  13. [13] A. Yu. Olshanskiĭ, Geometry of Defining Relations in Groups, Nauka, Moscow, 1989 (in Russian). 
  14. [14] J.-P. Serre, Trees, Springer, New York, 1980. 
  15. [15] V. P. Shunkov, On periodic groups with almost regular involutions, Algebra i Logika 11 (1972), 470-493 (in Russian). 
  16. [16] A. I. Sozutov, On groups with Frobenius pairs, ibid. 16 (1977), 204-212 (in Russian). 
  17. [17] A. I. Sozutov and V. P. Shunkov, On infinite groups with Frobenius subgroups, ibid. 16 (1977), 711-735 (in Russian). Zbl0405.20040

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