Let $ G$ be a finite group, and $ p$ a prime number; a character of $ G$ is called $ p$-constant if it takes a constant value on all the elements of $ G$ whose order is divisible by $ p$. This is a generalization of the very important concept of characters of $ p$-defect zero. In this paper, we characterize the finite $ p$-solvable groups having a faithful irreducible character that is $ p$-constant and not of $ p$-defect zero, and we will show that a non-$ p$-solvable group with this property is an almost-simple group.
On groups having a p-constant character / Dolfi, S., Pacifici, E.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 149:(2021), pp. 107-120. [10.1090/proc/15256]
On groups having a p-constant character
Dolfi S.
;Pacifici E.
2021
Abstract
Let $ G$ be a finite group, and $ p$ a prime number; a character of $ G$ is called $ p$-constant if it takes a constant value on all the elements of $ G$ whose order is divisible by $ p$. This is a generalization of the very important concept of characters of $ p$-defect zero. In this paper, we characterize the finite $ p$-solvable groups having a faithful irreducible character that is $ p$-constant and not of $ p$-defect zero, and we will show that a non-$ p$-solvable group with this property is an almost-simple group.File | Dimensione | Formato | |
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P-ConstantCharacters.pdf
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p-constant-characters_revised.pdf
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