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).
@article{bwmeta1.element.doi-10_2478_s11533-007-0030-4,
author = {B. Wehrfritz},
title = {The abelianization of hypercyclic groups},
journal = {Open Mathematics},
volume = {5},
year = {2007},
pages = {686-695},
zbl = {1147.20029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0030-4}
}
B. Wehrfritz. The abelianization of hypercyclic groups. Open Mathematics, Tome 5 (2007) pp. 686-695. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0030-4/
[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 | Zbl 1105.20030
[2] D.J.S. Robinson: Finiteness conditions and generalized soluble groups, Springer-Verlag, New York-Berlin, 1972. | Zbl 0243.20032
[3] B.A.F. Wehrfritz: Infinite linear groups, Springer-Verlag, New York-Heidelberg, 1973. | Zbl 0261.20038
[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 | Zbl 1133.20021