A new characterization of projective special linear groups \(L_3(q)\)

Abstract

In this paper, we prove that projective special linear groups \(L_3(q)\), where \(0<q=5k\pm 2\) \((k\in\mathbb{ Z})\) and \(q^2+q+1\) is a~prime number can be uniquely determined by their order and the number of elements with same order.