Table of Contents
ISRN Algebra
Volume 2011, Article ID 868096, 20 pages
http://dx.doi.org/10.5402/2011/868096
Research Article

On Irreducible Linear Groups of Nonprimary Degree

Institute of Mathematics of the National Academy of Sciences of the Republic of Belarus, Kirova Street 32a, 246000 Gomel, Belarus

Received 6 May 2011; Accepted 5 June 2011

Academic Editor: A. Vourdas

Copyright © 2011 A. A. Yadchenko. 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

It is established that degree 2|𝐴|+1 of irreducible complex linear group with the group 𝐴 of cosimple automorphisms of odd order is a prime number and proved that if degree 2|𝐻|+1 of πœ‹-solvable irreducible complex linear group 𝐺 with a πœ‹-Hall 𝑇𝐼-subgroup 𝐻 is not a prime power, then 𝐻 is Abelian and normal in 𝐺.