IJPAM: Volume 91, No. 4 (2014)

ON CONJUGACY AND ORDER STRUCTURE OF
CERTAIN CLASSES OF FINITE GROUPS

Osango E.O. Hesbon$^1$, Owino Maurice Oduor$^2$
$^1$Department of Mathematics
Egerton University
P.O. Box 536, Egerton, KENYA
$^2$Department of Mathematics and Computer Science
University of Kabianga
P.O. Box 2030-20200, Kericho, KENYA


Abstract. The classification of finite groups still remains an open problem. The concept of conjugacy provides an insight on the structure of finite groups. It is an equivalence relation which provides a neat algebraic description of the size of each conjugacy class in a finite group. We set to examine the conjugacy and order structures of general linear groups, \(GL(n,q)\) and special linear groups, \(SL(n,q)\) with some restrictions on \(n\). We have also established the special cases of conjugacy classes of \(GL(n,q)\) splitting in \(SL(n,q)\) and given the conditions of splitting or not splitting.

Received: October 23, 2013

AMS Subject Classification: 20E45, 20H30

Key Words and Phrases: conjugacy classes, finite groups

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DOI: 10.12732/ijpam.v91i4.2 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 4