INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 3, Issue 1 , March 2014

Pages: 85-98

Date of Publication: 01-Mar-2014

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ON THE ORDER STRUCTURE OF CYCLIC AND DIHEDRAL SUBGROUPS EMBEDDED IN GL(n,q)

Author: OSANGO HESBON E. O.*

Category: Engineering, Science and Mathematics

Abstract:

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 order structure of cyclic and dihedral subgroups embedded in GL(n,q) for n = 2, 3. We strived to determine all possible orders of various elements of GL(n,q) and their divisors by looking at their characteristic and minimal polynomials and using the fact that matrices with the same Jordan form are similar and hence conjugate under certain conditions.

Keywords: Jordan Canonical Form, Extension field, conjugacy, order structure