The abelianization of hypercyclic groups

B. Wehrfritz

Open Mathematics (2007)

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

Abstract

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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).

How to cite

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B. 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

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  1. [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. [2] D.J.S. Robinson: Finiteness conditions and generalized soluble groups, Springer-Verlag, New York-Berlin, 1972. Zbl0243.20032
  3. [3] B.A.F. Wehrfritz: Infinite linear groups, Springer-Verlag, New York-Heidelberg, 1973. Zbl0261.20038
  4. [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

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