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

Document Type : Research Paper

Authors

1 Department of Economics and Management, Shanghai University of Political Science and Law, Shanghai 201701, China

2 Department of Mathematics, Chongqing University of Arts and Sciences, Chongqing 402160, China3School of Mathe- matics, Suzhou University, Suzhou 215006, China

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.

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Main Subjects

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