This article is cited in 4 papers

Mathematical logic, algebra and number theory

Some simple groups which are determined by their character degree graphs

S. Heydari, N. Ahanjideh

Department of pure Mathematics, Faculty of Mathematical Sciences, Shahre-kord University, P. O. Box 115, Shahre-kord, Iran

Abstract: Let $G$ be a finite group, and let $\rho(G)$ be the set of prime divisors of the irreducible character degrees of $G$. The character degree graph of $G$, denoted by $\Delta(G)$, is a graph with vertex set $\rho(G)$ and two vertices $a$ and $b$ are adjacent in $\Delta(G)$, if $ab$ divides some irreducible character degree of $G$. In this paper, we are going to show that some simple groups are uniquely determined by their orders and character degree graphs. As a consequence of this paper, we conclude that $M_{12}$ is not determined uniquely by its order and its character degree graph.

Keywords: character degree, minimal normal subgroup, Sylow subgroup.

UDC: 512.542.5

MSC: 20C15, 20E99

Received September 21, 2016, published December 23, 2016

Language: English

DOI: 10.17377/semi.2016.13.101

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