# The abelianization of hypercyclic groups

Open Mathematics (2007)

- Volume: 5, Issue: 4, page 686-695
- ISSN: 2391-5455

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topB. Wehrfritz. "The abelianization of hypercyclic groups." Open Mathematics 5.4 (2007): 686-695. <http://eudml.org/doc/269256>.

@article{B2007,

abstract = {Let G be a hypercyclic group. The most substantial results of this paper are the following. a) If G/G′ is 2-divisible, then G is 2-divisible. b) If G/G′ is a 2′-group, then G is a 2′-group. c) If G/G′ is divisible by finite-of-odd-order, then G/V is divisible by finite-of-odd-order, where V is the intersection of the lower central series (continued transfinitely) of O 2′ (G).},

author = {B. Wehrfritz},

journal = {Open Mathematics},

keywords = {hypercyclic group; divisible-by-finite group; hypercyclic groups; hypercentral groups; divisible-by-finite groups; lower central series},

language = {eng},

number = {4},

pages = {686-695},

title = {The abelianization of hypercyclic groups},

url = {http://eudml.org/doc/269256},

volume = {5},

year = {2007},

}

TY - JOUR

AU - B. Wehrfritz

TI - The abelianization of hypercyclic groups

JO - Open Mathematics

PY - 2007

VL - 5

IS - 4

SP - 686

EP - 695

AB - Let G be a hypercyclic group. The most substantial results of this paper are the following. a) If G/G′ is 2-divisible, then G is 2-divisible. b) If G/G′ is a 2′-group, then G is a 2′-group. c) If G/G′ is divisible by finite-of-odd-order, then G/V is divisible by finite-of-odd-order, where V is the intersection of the lower central series (continued transfinitely) of O 2′ (G).

LA - eng

KW - hypercyclic group; divisible-by-finite group; hypercyclic groups; hypercentral groups; divisible-by-finite groups; lower central series

UR - http://eudml.org/doc/269256

ER -

## References

top- [1] L. Heng, Z. Duan and G. Chen: “On hypercentral groups G with |G: G n| < ∞”, Comm. Algebra, Vol. 34, (2006), no. 5, pp. 1803–1810. http://dx.doi.org/10.1080/00927870500542770 Zbl1105.20030
- [2] D.J.S. Robinson: Finiteness conditions and generalized soluble groups, Springer-Verlag, New York-Berlin, 1972. Zbl0243.20032
- [3] B.A.F. Wehrfritz: Infinite linear groups, Springer-Verlag, New York-Heidelberg, 1973. Zbl0261.20038
- [4] B.A.F. Wehrfritz: “On hypercentral groups”, Cent. Eur. J. Math., Vol. 5, (2007), no. 3, pp. 596–606. http://dx.doi.org/10.2478/s11533-007-0015-3 Zbl1133.20021