University of Isfahan International Journal of Group Theory 2251-7650 7 1 2018 03 01 Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements 17 21 21220 10.22108/ijgt.2017.21220 EN Andrea Lucchini Dipartimento di Matematica Università di Padova Journal Article 2016 07 18 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. ‎Character degrees class sizes https://ijgt.ui.ac.ir/article_21220_7d6849ef0c0f20d2874ee36c05cf3ef1.pdf