Characterization of some alternating groups by order and largest element order

Document Type : Original Article

Authors

Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

The prime graph (or Gruenberg-Kegel graph) of a finite group is a well-known graph. In this paper, first, we investigate the structure of the finite groups with a non-complete prime graph. Then as an application, we prove that every alternating group An, where n31 is determined by its order and its largest element order. Also, we show that A32 is not characterizable by order and the largest element order.

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Main Subjects


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