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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 1, 2007

The abelianization of hypercyclic groups

  • B. Wehrfritz EMAIL logo
From the journal Open Mathematics

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).

MSC: 20F19

[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/10.1080/0092787050054277010.1080/00927870500542770Search in Google Scholar

[2] D.J.S. Robinson: Finiteness conditions and generalized soluble groups, Springer-Verlag, New York-Berlin, 1972. 10.1007/978-3-662-07241-7Search in Google Scholar

[3] B.A.F. Wehrfritz: Infinite linear groups, Springer-Verlag, New York-Heidelberg, 1973. 10.1007/978-3-642-87081-1Search in Google Scholar

[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/s11533-007-0015-310.2478/s11533-007-0015-3Search in Google Scholar

Published Online: 2007-12-1
Published in Print: 2007-12-1

© 2007 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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