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A CHARACTER-THEORETIC CRITERION FOR THE SOLVABILITY OF FINITE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  20 January 2016

YAN-JUN LIU  and
YANG LIU
YAN-JUN LIU*
Affiliation:
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, PR China email liuyj@math.pku.edu.cn
YANG LIU
Affiliation:
Beijing International Center for Mathematical Research, Peking University, Beijing 100871, PR China email liuyang@math.pku.edu.cn
*
✉liuyj@math.pku.edu.cn
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Abstract

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Let $p$ be an odd prime. In this note, we show that a finite group $G$ is solvable if all degrees of irreducible complex characters of $G$ not divisible by $p$ are either 1 or a prime.

Keywords

finite groupirreducible charactersolvabilitycharacter degree

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 94 , Issue 1 , August 2016 , pp. 30 - 35
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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