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ON THE ORDERS OF ZEROS OF STRONGLY MONOLITHIC CHARACTERS

Part of: Representation theory of groups

Published online by Cambridge University Press:  12 December 2025

GAMZE AKAR Open the ORCID record for GAMZE AKAR [Opens in a new window]  and
TEMHA ERKOÇ Open the ORCID record for TEMHA ERKOÇ [Opens in a new window]
GAMZE AKAR
Affiliation:
Institute of Graduate Studies in Sciences, Istanbul University , Istanbul 34134, Türkiye e-mail: gamze_akar_1995@hotmail.com
TEMHA ERKOÇ*
Affiliation:
Department of Mathematics, Faculty of Science, Istanbul University , 34134 Istanbul, Türkiye
*
e-mail: erkoct@istanbul.edu.tr
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Abstract

Let G be a finite group and p be a prime number. An element g of G is called an $\mathrm {SM}^*$-vanishing element of G if there exists a strongly monolithic character $\chi $ of G satisfying $Z(\chi )=\ker \chi $ and $\chi (g)=0$. In this paper, we present some results on the relationship between the orders of $\mathrm {SM}^*$-vanishing elements of G and the structure of G.

Keywords

finite groupsstrongly monolithic charactersvanishing element

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 8
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

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Footnotes

This work was supported by the Scientific and Technological Research Council of Türkiye (TÜBİTAK). The project number is 123F260.

References

Berkovich, Y. G. and Zhmud’, E. M., Characters of Finite Groups, Part 2, Translations of Mathematical Monographs, 181 (American Mathematical Society, Providence, RI, 1997).10.1090/mmono/172CrossRefGoogle Scholar
Bianchi, M., Chillag, D., Lewis, M. L. and Pacifici, E., ‘Character degree graphs that are complete graphs’, Proc. Amer. Math. Soc. 135 (2007), 671–676.10.1090/S0002-9939-06-08651-5CrossRefGoogle Scholar
Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, with Computational Assistance from J. G. Thackray (Clarendon Press, Oxford, 1985).Google Scholar
Dolfi, S., Malle, G. and Navarro, G., ‘The finite groups with no real $p$ -elements’, Israel J. Math. 192 (2012), 831–840.10.1007/s11856-012-0054-8CrossRefGoogle Scholar
Dolfi, S., Navarro, G. and Tiep, P. H., ‘Primes dividing the degrees of the real characters’, Math. Z. 259 (2008), 755–774.10.1007/s00209-007-0247-8CrossRefGoogle Scholar
Dolfi, S., Pacifici, E., Sanus, L. and Spiga, P., ‘On the orders of zeros of irreducible characters’, J. Algebra 321 (2009), 345–352.10.1016/j.jalgebra.2008.10.004CrossRefGoogle Scholar
Erkoç, T., Bozkurt Güngör, S. and Akar, G., ‘SM-vanishing conjugacy classes of finite groups’, J. Algebra Appl. 24(2) (2025), Article no. 2550047.10.1142/S0219498825500471CrossRefGoogle Scholar
Erkoç, T., Bozkurt Güngör, S. and Özkan, J. M., ‘Strongly monolithic characters of finite groups’, J. Algebra Appl. 22(8) (2023), Article no. 2350176.10.1142/S0219498823501761CrossRefGoogle Scholar
Granville, A. and Ono, K., ‘Defect zero $p$ -blocks for finite simple groups’, Trans. Amer. Math. Soc. 348 (1996), 331–347.10.1090/S0002-9947-96-01481-XCrossRefGoogle Scholar
Huppert, B., Endliche Gruppen 1 (Springer, Berlin, 1967).10.1007/978-3-642-64981-3CrossRefGoogle Scholar
Isaacs, I. M., Character Theory of Finite Groups (Academic Press, New York, 1976).Google Scholar
Navarro, G., Character Theory and the McKay Conjecture (Cambridge University Press, Cambridge, 2018).10.1017/9781108552790CrossRefGoogle Scholar
Navarro, G., Sanus, L. and Tiep, P. H., ‘Real characters and degrees’, Israel J. Math. 171 (2009), 157–173.10.1007/s11856-009-0045-6CrossRefGoogle Scholar
Özkan, J. M. and Erkoç, T., ‘On the relations between the structures of finite groups and their strongly monolithic characters’, Comm. Algebra 51(2) (2023), 657–662.10.1080/00927872.2022.2107214CrossRefGoogle Scholar