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.
544
454
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Grittini
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/1222883
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