The abelianization of hypercyclic groups

• Autorzy: B. Wehrfritz
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

hypercyclic group; divisible-by-finite group

Kategorie tematyczne

• 20F19: Generalizations of solvable and nilpotent groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 4
• Strony: 686-695

Daty

wydano

2007-12-01

online

2007-12-01

Twórcy

autor

B. Wehrfritz

• University of London

Bibliografia

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

Identyfikatory

DOI

10.2478/s11533-007-0030-4