Geodesic
A solvability criterion for finite groups related to character degrees
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1205-1209.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/CMJ.2020.0440-19
Classification : 20C15, 20D10
Keywords: non-solvable group; solvable group; character degree 
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Miraali, Babak; Robati, Sajjad Mahmood. A solvability criterion for finite groups related to character degrees. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1205-1209. doi : 10.21136/CMJ.2020.0440-19. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0440-19/

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