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SOME CRITERIA FOR SOLVABILITY AND NILPOTENCY OF FINITE GROUPS BY STRONGLY MONOLITHIC CHARACTERS

Part of: Representation theory of groups

Published online by Cambridge University Press:  22 September 2022

SULTAN BOZKURT GÜNGÖR Open the ORCID record for SULTAN BOZKURT GÜNGÖR [Opens in a new window]  and
TEMHA ERKOÇ Open the ORCID record for TEMHA ERKOÇ [Opens in a new window]
SULTAN BOZKURT GÜNGÖR
Affiliation:
Department of Mathematics, Faculty of Science, Istanbul University, 34134 Istanbul, Turkey e-mail: sultan__bozkurt@hotmail.com
TEMHA ERKOÇ*
Affiliation:
Department of Mathematics, Faculty of Science, Istanbul University, 34134 Istanbul, Turkey
*
e-mail: erkoctemha@gmail.com
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Abstract

Gagola and Lewis [‘A character theoretic condition characterizing nilpotent groups’, Comm. Algebra 27 (1999), 1053–1056] proved that a finite group G is nilpotent if and only if $\chi (1)^{2}$ divides $\lvert G:\textrm {ker}\,\chi \rvert $ for every irreducible character $\chi $ of G. The theorem was later generalised by using monolithic characters. We generalise the theorem further considering only strongly monolithic characters. We also give some criteria for solvability and nilpotency of finite groups by their strongly monolithic characters.

Keywords

finite groupsolvable groupnilpotent groupstrongly monolithic character

MSC classification

Primary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 1 , August 2023 , pp. 120 - 124
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The work of the authors was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK), project number 119F295.

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