A new characterization of \(L_2\)(q) where q = \(p^n\) < 125

Abstract

It is a well-known topic to characterize a ¯nite simple group by using two quantities, the order of G and π_e(G) in the past 30 years, where π_e(G) denotes the set of orders of elements in G. Recently this topic has been finished by V.D. Mazurov, et al. Here the authors will try to characterize some finite simple groups by using less quantities and have successfully characterized L₂(q), where q = pⁿ < 125, by using the order of L₂(q) and the three largest element orders of L₂(q).