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.
Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements
Lucchini, Andrea
2018
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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