On hypercentral groups

B. Wehrfritz

Open Mathematics (2007)

  • Volume: 5, Issue: 3, page 596-606
  • ISSN: 2391-5455

Abstract

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Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.

How to cite

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B. Wehrfritz. "On hypercentral groups." Open Mathematics 5.3 (2007): 596-606. <http://eudml.org/doc/269316>.

@article{B2007,
abstract = {Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.},
author = {B. Wehrfritz},
journal = {Open Mathematics},
keywords = {hypercentral group; divisible-by-finite group; hypercentral groups; divisible-by-finite groups; divisible Abelian groups; subgroups of finite index},
language = {eng},
number = {3},
pages = {596-606},
title = {On hypercentral groups},
url = {http://eudml.org/doc/269316},
volume = {5},
year = {2007},
}

TY - JOUR
AU - B. Wehrfritz
TI - On hypercentral groups
JO - Open Mathematics
PY - 2007
VL - 5
IS - 3
SP - 596
EP - 606
AB - Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.
LA - eng
KW - hypercentral group; divisible-by-finite group; hypercentral groups; divisible-by-finite groups; divisible Abelian groups; subgroups of finite index
UR - http://eudml.org/doc/269316
ER -

References

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  1. [1] L. Fuchs: Infinite Abelian Groups, Vol. 1, Academic Press, New York, 1970. Zbl0209.05503
  2. [2] L. Heng, Z. Duan and G. Chen: “On hypercentral groups G with |G: G m | < ∞”, Comm. Algebra, Vol. 34, (2006), pp. 1803–1810. http://dx.doi.org/10.1080/00927870500542770 Zbl1105.20030
  3. [3] O.H. Kegel and B.A.F. Wehrfritz: Locally Finite Groups, North-Holland, Amsterdam, 1973. 
  4. [4] D.H. McLain: “Remarks on the upper central series of a group”, Proc. Glasgow Math. Assoc., Vol. 3, (1956), pp. 38–44. http://dx.doi.org/10.1017/S2040618500033414 Zbl0072.25702
  5. [5] D.J.S. Robinson: Finiteness Conditions and Generalized Soluble Groups, Springer-Verlag, Berlin, 1972. Zbl0243.20032
  6. [6] B.A.F. Wehrfritz: “Nilpotence in finitary linear groups”, Michigan Math. J., Vol. 40, (1992), pp. 419–432. Zbl0807.20040

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