A Solvability Criterion for Finite Groups Related to Character Degrees

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 A7 or S7 by a solvable group.

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Correspondence to Sajjad Mahmood Robati.

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Miraali, B., Robati, S.M. A Solvability Criterion for Finite Groups Related to Character Degrees. Czech Math J 70, 1205–1209 (2020). https://doi.org/10.21136/CMJ.2020.0440-19

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Keywords

  • non-solvable group
  • solvable group
  • character degree

MSC 2020

  • 20C15
  • 20D10