On hypercentral groups

• Autorzy: B. Wehrfritz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hypercentral group; divisible-by-finite group

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 3
• Strony: 596-606

Daty

wydano

2007-09-01

online

2007-05-26

Twórcy

autor

B. Wehrfritz

• University of London

Bibliografia

• [1] L. Fuchs: Infinite Abelian Groups, Vol. 1, Academic Press, New York, 1970.
• [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
• [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
• [5] D.J.S. Robinson: Finiteness Conditions and Generalized Soluble Groups, Springer-Verlag, Berlin, 1972.
• [6] B.A.F. Wehrfritz: “Nilpotence in finitary linear groups”, Michigan Math. J., Vol. 40, (1992), pp. 419–432.

Identyfikatory

DOI

10.2478/s11533-007-0015-3