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.

Grittini, N., p-length and character degrees in p-solvable groups, <<JOURNAL OF ALGEBRA>>, 2020; 544 (February): 454-462. [doi:10.1016/j.jalgebra.2019.09.034] [http://hdl.handle.net/10807/188779]

p-length and character degrees in p-solvable groups

Grittini, N.
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.
Inglese
Grittini, N., p-length and character degrees in p-solvable groups, <<JOURNAL OF ALGEBRA>>, 2020; 544 (February): 454-462. [doi:10.1016/j.jalgebra.2019.09.034] [http://hdl.handle.net/10807/188779]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/188779
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