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NONDIVISIBILITY AMONG IRREDUCIBLE CHARACTER CO-DEGREES

Part of: Representation theory of groups

Published online by Cambridge University Press:  24 May 2021

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

For a character $\chi $ of a finite group G, the number $\chi ^c(1)={[G:{\textrm {ker}}\chi ]}/{\chi (1)}$ is called the co-degree of $\chi $ . A finite group G is an ${\textrm {NDAC}} $ -group (no divisibility among co-degrees) when $\chi ^c(1) \nmid \phi ^c(1)$ for all irreducible characters $\chi $ and $\phi $ of G with $1< \chi ^c(1) < \phi ^c(1)$ . We study finite groups admitting an irreducible character whose co-degree is a given prime p and finite nonsolvable ${\textrm {NDAC}} $ -groups. Then we show that the finite simple groups $^2B_2(2^{2f+1})$ , where $f\geq 1$ , $\mbox {PSL}_3(4)$ , ${\textrm {Alt}}_7$ and $J_1$ are determined uniquely by the set of their irreducible character co-degrees.

Keywords

co-degree of a characternonsolvable NDAC-group

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20D05: Finite simple groups and their classification
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 68 - 74
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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