Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements

Document Type : Ischia Group Theory 2016


Dipartimento di Matematica Università di Padova


We prove that every finite group $G$ contains a three-generated subgroup $H$ with the following property‎: ‎a prime $p$ divides the degree of an irreducible character of $G$ if and only if it divides the degree of an irreducible character of $H.$ There is no analogous result for the prime divisors of the sizes of the conjugacy classes‎.


Main Subjects

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Volume 7, Issue 1 - Serial Number 1
Proceedings of the Ischia Group Theory 2016-Part I
March 2018
Pages 17-21
  • Receive Date: 18 July 2016
  • Revise Date: 13 February 2017
  • Accept Date: 13 October 2016
  • Published Online: 01 March 2018