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$p$-DIVISIBILITY OF CO-DEGREES OF IRREDUCIBLE CHARACTERS

Part of: Representation theory of groups

Published online by Cambridge University Press:  07 April 2020

ROYA BAHRAMIAN Open the ORCID record for ROYA BAHRAMIAN [Opens in a new window]  and
NEDA AHANJIDEH Open the ORCID record for NEDA AHANJIDEH [Opens in a new window]
ROYA BAHRAMIAN
Affiliation:
Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran email [email protected]
NEDA AHANJIDEH*
Affiliation:
Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran email [email protected]
*
✉[email protected]
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Abstract

For a character $\unicode[STIX]{x1D712}$ of a finite group $G$, the co-degree of $\unicode[STIX]{x1D712}$ is $\unicode[STIX]{x1D712}^{c}(1)=[G:\text{ker}\unicode[STIX]{x1D712}]/\unicode[STIX]{x1D712}(1)$. We study finite groups whose co-degrees of nonprincipal (complex) irreducible characters are divisible by a given prime $p$.

Keywords

co-degree of a characterco-prime actionp-solvable groups

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 78 - 82
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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