International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 12, Pages 707-714
On minimal artinian modules and minimal artinian linear groups
1Mathematics Department, Dnepropetrovsk University, Provulok Naukovyi 13, Dnepropetrovsk 49050, Ukraine
2Mathematics Department, National University, 9920 S. La Cienega Blvd, Inglewood 90301, CA, USA
Received 19 March 2001
Copyright © 2001 Leonid A. Kurdachenko and Igor 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.
The paper is devoted to the study of some important types of
minimal artinian linear groups. The authors prove that in such classes of groups as hypercentral groups (so also, nilpotent and abelian groups) and -groups, minimal artinian linear groups have precisely the same structure as the corresponding irreducible linear groups.