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arXiv · 1307.2175

Finite groups whose prime graphs are regular

Hung P. Tong-Viet
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Abstract

Let G be a finite group and let Irr(G) be the set of all irreducible complex characters of G. Let cd(G) be the set of all character degrees of G and denote by \rho(G) the set of primes which divide some character degrees of G. The prime graph \Delta(G) associated to G is a graph whose vertex set is \rho(G) and there is an edge between two distinct primes p and q if and only if the product pq divides some character degree of G. In this paper, we show that the prime graph \Delta(G) of a finite group G is 3-regular if and only if it is a complete graph with four vertices.

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Hung P. Tong-Viet. 2013-07-05. Finite groups whose prime graphs are regular. https://arxiv.org/abs/1307.2175

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