Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 1205-1209, 2020
A solvability criterion for finite groups related to character degrees
Babak Miraali, Sajjad Mahmood Robati
Received October 1, 2019. Published online September 18, 2020.
Abstract: Let $m>1$ be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly $m$ prime divisors. We show that such groups are solvable whenever $m>2$. Moreover, we prove that if $G$ is a non-solvable group with this property, then $m=2$ and $G$ is an extension of ${\rm A}_7$ or ${\rm S}_7$ by a solvable group.
Keywords: non-solvable group; solvable group; character degree
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