The abelianization of hypercyclic groups

B. Wehrfritz

Open Mathematics (2007)

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

Abstract

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.