4-Regular prime graphs of nonsolvable groups

Abstract

Let $G$ be a finite group and $\text{cd}(G)$ denote the character degree set for $G$. The prime graph $\Delta (G)$ is a simple graph whose vertex set consists of prime divisors of elements in $\text{cd}(G)$, denoted $\rho (G)$. Two primes $p,q\in \rho (G)$ are adjacent in $\Delta (G)$ if and only if $pq|a$ for some $a\in \text{cd}(G)$. We determine which simple 4-regular graphs occur as prime graphs for some finite nonsolvable group.

36 pages,

References in corpus (2)

• Groups whose prime graphs have no triangles
• Square character degree graphs yield direct products