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
Classification MSC:  20C15, 20D10
DOI:  10.21136/CMJ.2020.0440-19


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Affiliations:   Babak Miraali, Sajjad Mahmood Robati (corresponding author), Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, 34148-96818, Qazvin, Iran, e-mail: babak.miraali@gmail.com, mahmoodrobati@sci.ikiu.ac.ir, sajjad.robati@gmail.com


 
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