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, Nicola
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:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
