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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1989-1994
http://dx.doi.org/10.1155/IJMMS.2005.1989

On Semiabelian Groups

1Algebra Department, Institute of Mathematics, National Academy of Science, 3 Tereshenkivska Street, Kyiv-4 01601, Ukraine
2Department of Mathematics, National University, 9920 South La Cienega Boulevard, Inglewood 90301, CA, USA

Received 21 June 2004; Revised 25 August 2004

Copyright © 2005 N. F. Kuzennyi and I. Ya. Subbotin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish some structural results on the semiabelian groups, that is, groups generated by their cyclic normal subgroups. Such groups play a significant role in the theory of supersoluble groups. A description of two-generated semiabelian groups and torsion-free semiabelian groups is obtained.