Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements
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 o...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2018-03-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://ijgt.ui.ac.ir/article_21220_7d6849ef0c0f20d2874ee36c05cf3ef1.pdf |
| Summary: | 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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| ISSN: | 2251-7650 2251-7669 |