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.

**Keywords**

**Main Subjects**

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March 2022

Pages 17-22

**Receive Date:**25 July 2020**Revise Date:**01 April 2021**Accept Date:**01 April 2021**Published Online:**01 March 2022