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

Colloquium Mathematicae (1999)

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

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topIvanov, 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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- [5] H. Furstenberg, Poincaré recurrence and number theory, Bull. Amer. Math. Soc. 5 (1981), 211-234. Zbl0481.28013
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- [8] R. Grigorchuk, An example of a finitely presented amenable group not belonging to the class $EG$, ibid. 189 (1998), 79-100 (in Russian). Zbl0931.43003
- [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] M. Kargapolov and Yu. Merzlyakov, Basic Group Theory, Nauka, Moscow, 1977 (in Russian). Zbl0499.20001
- [11] P. Longobardi, M. Maj and A. H. Rhemtulla, Groups with no free subsemigroups, Proc. Amer. Math. Soc., to appear. Zbl0833.20043
- [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). Zbl0405.20040

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