Characterizations of Chevalley groups using order of the finite groups

Abid Mahboob\(^1\)
Department of Mathematics, Division of Science and Technology, University of Education Lahore, Pakistan.
Taswer Hussain
GHSS Shergarh, Okara Pakistan.
Misbah Akram
Department of Mathematics, GCU, Lahore, Pakistan.
Sajid Mahboob
Department of Mathematics, The University of Education Lahore, Pakistan.
Nasir Ali
Department of Mathematics, The University of Education Lahore, Pakistan.
Ali Raza
Department of Mathematics, The University of Education Lahore, Pakistan.
\(^{1}\)Corresponding Author: abid.mahboob@ue.edu.pk
Copyright © 2020 Abid Mahboob, Taswer Hussain, Misbah Akram, Sajid Mahboob, Nasir Ali, Ali Raza. 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.

Submitted: 20 December 2019; Accepted: 12 March 2020; Published: 19 March 2020.

Abstract

In this paper, we prove \(\psi (A_{1}(4))< \psi(G)\), \( \forall \) groups which are not simple with order sixty, \( A_{1}(4) \) is Chevalley group (Linear group) of order 60. Also we prove that \( \psi (A_{2}(2))< \psi(G)\) using higher order non-simple groups of order 168.

Keywords:

Chevalley groups, Finite groups, Simple groups, Element orders.