Let G be a p-solvable group, where p is a prime. We prove that the p-length of G is less or equal then the number of distinct irreducible character degrees of G not divisible by p. Furthermore, we prove that the result still holds if we impose some restriction on the field of values of the characters. In particular, if p=2, we can consider only rational-valued characters.
p-length and character degrees in p-solvable groups / Grittini. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - ELETTRONICO. - 544:(2020), pp. 454-462. [10.1016/j.jalgebra.2019.09.034]
p-length and character degrees in p-solvable groups
Grittini
2020
Abstract
Let G be a p-solvable group, where p is a prime. We prove that the p-length of G is less or equal then the number of distinct irreducible character degrees of G not divisible by p. Furthermore, we prove that the result still holds if we impose some restriction on the field of values of the characters. In particular, if p=2, we can consider only rational-valued characters.File in questo prodotto:
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