LetGbe a finite group, andpa prime number; a character ofGis calledp-constantif it takes a constant value on all the elements ofGwhose order is divisible byp. This is ageneralization of the very important concept of characters ofp-defect zero. In this paper, wecharacterize the finitep-solvable groups having a faithful irreducible character that isp-constantand not ofp-defect zero, and we will show that a non-p-solvable group with this property is analmost-simple group.
On groups having a $p$-constant character / S. Dolfi, E. Pacifici, L. Sanus. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - (2020). [Epub ahead of print] [10.1090/proc/15256]
On groups having a $p$-constant character
E. PacificiSecondo
;
2020
Abstract
LetGbe a finite group, andpa prime number; a character ofGis calledp-constantif it takes a constant value on all the elements ofGwhose order is divisible byp. This is ageneralization of the very important concept of characters ofp-defect zero. In this paper, wecharacterize the finitep-solvable groups having a faithful irreducible character that isp-constantand not ofp-defect zero, and we will show that a non-p-solvable group with this property is analmost-simple group.File | Dimensione | Formato | |
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