Lucchini, A. (2018). Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements. International Journal of Group Theory, 7(1), 17-21. doi: 10.22108/ijgt.2017.21220

Andrea Lucchini. "Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements". International Journal of Group Theory, 7, 1, 2018, 17-21. doi: 10.22108/ijgt.2017.21220

Lucchini, A. (2018). 'Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements', International Journal of Group Theory, 7(1), pp. 17-21. doi: 10.22108/ijgt.2017.21220

Lucchini, A. Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements. International Journal of Group Theory, 2018; 7(1): 17-21. doi: 10.22108/ijgt.2017.21220

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

^{}Dipartimento di Matematica
Università di Padova

Abstract

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.

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