A New Characterization of SimpleK3-Groups

It is a well-known topic to characterize a finite 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 Mazurov et al. Here the authors will try to characterize some finite simple groups by using less quantities and have successfully characterized simple K 3-groups by using the order of a group and the largest and the second largest element orders, where a K 3-group is a group of order containing exactly three distinct primes.