The recognition of finite simple groups with no elements of order $10$ by their element orders

Abstract

The spectrum of a finite group is the set of‎ ‎its element orders‎. ‎$H$ is said to be a finite cover of $G$ if $G$‎ ‎is a homomorphic image of $H$ and $H$ is finite‎. ‎The main aim of‎ ‎this article is to characterize the finite simple groups with no‎ ‎elements of order 10 by its spectrum among covers‎. ‎At the same‎ ‎time‎, ‎above simple groups are completely classified‎. ‎At last‎, ‎some‎ ‎results on the recognition by spectrum of above groups are also‎ ‎achieved‎.

Keywords

• recognition‎
• ‎spectrum‎
• ‎simple group‎
• ‎cover