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Notes on normal p-complements and monomial characters


Xiaoyou Chen
Yong Yong

Abstract

Let G be a finite group and Irr(G) be the set of irreducible (complex) characters of G. Let X ∈  Irr(G) and write cod(X) = |G : ker X |/x(1) as the codegree of X , where ker X is the kernel of X. Denote by M(G) the intersection of the kernels of all the monolithic, monomial irreducible characters of a p-solvable group G with codegrees divisible by a prime p. We prove in this note that M(G) has a normal p-complement, and then the theorem in [2] is generalized. Also, we prove that about the theorem in [2] more is true.


Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606