# On hypercentral groups

Open Mathematics (2007)

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

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topB. 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

top- [1] L. Fuchs: Infinite Abelian Groups, Vol. 1, Academic Press, New York, 1970. Zbl0209.05503
- [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] O.H. Kegel and B.A.F. Wehrfritz: Locally Finite Groups, North-Holland, Amsterdam, 1973.
- [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] D.J.S. Robinson: Finiteness Conditions and Generalized Soluble Groups, Springer-Verlag, Berlin, 1972. Zbl0243.20032
- [6] B.A.F. Wehrfritz: “Nilpotence in finitary linear groups”, Michigan Math. J., Vol. 40, (1992), pp. 419–432. Zbl0807.20040