This article is cited in 3 papers

On characterization by order and prime graph for alternating groups

A. Mahmoudifar^a, B. Khosravi<sup>ab

a</sup> Department of Pure Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
^b School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

Abstract: There are some graphs related to the structure of a finite group, e.g. the prime graph, the solvable graph, and the noncommuting graph of a finite group. In this paper, we consider characterization by order and prime graph for alternating groups. In particular, we show that there exists a closed relation between characterization by order and prime graph of some of the alternating groups and Goldbach's conjecture. Also by using the main results, we answer some conjectures and a problem about characterization by order and degree pattern for alternating and symmetric groups that are stated in [R. Kogani-Moghaddam and A. R. Moghaddamfar, Groups with the same order and degree pattern, Sci. China Math., 2012].

Keywords: alternating group, symmetric group, solvable graph, prime graph, degree pattern, Goldbach's conjecture.

UDC: 512.54

Received: 01.06.2013

 English version: Siberian Mathematical Journal, 2015, 56:1, 125–131

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