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SOME PRODUCTS OF SUBGROUPS AND VANISHING CONJUGACY CLASS SIZES

Part of: Structure and classification of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  13 July 2022

ADOLFO BALLESTER-BOLINCHES Open the ORCID record for ADOLFO BALLESTER-BOLINCHES [Opens in a new window] ,
RAMÓN ESTEBAN-ROMERO Open the ORCID record for RAMÓN ESTEBAN-ROMERO [Opens in a new window] ,
SESUAI Y. MADANHA Open the ORCID record for SESUAI Y. MADANHA [Opens in a new window]  and
MARÍA C. PEDRAZA-AGUILERA Open the ORCID record for MARÍA C. PEDRAZA-AGUILERA [Opens in a new window]
ADOLFO BALLESTER-BOLINCHES
Affiliation:
Departament de Matemàtiques, Universitat de València, Dr. Moliner 50, Burjassot 46100, València, Spain e-mail: adolfo.ballester@uv.es
RAMÓN ESTEBAN-ROMERO
Affiliation:
Departament de Matemàtiques, Universitat de València, Dr. Moliner 50, Burjassot 46100, València, Spain e-mail: ramon.esteban@uv.es
SESUAI Y. MADANHA*
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
MARÍA C. PEDRAZA-AGUILERA
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Camino de Vera, València, Spain e-mail: mpedraza@mat.upv.es
*
e-mail: sesuai.madanha@up.ac.za
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Abstract

In this note, we investigate some products of subgroups and vanishing conjugacy class sizes of finite groups. We prove some supersolubility criteria for groups with restrictions on the vanishing conjugacy class sizes of their subgroups.

Keywords

mutually permutable productsvanishing conjugacy class sizessupersoluble groups

MSC classification

Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Secondary: 20C15: Ordinary representations and characters 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20E45: Conjugacy classes

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 271 - 275
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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

These results are a part of the R+D+i project supported by the Grant PGC2018-095140-B-I00, funded by the Ministry for Science and Innovation MCIN/AEI/10.13039/501100011033 and by ‘ERDF A way of making Europe’.

References

Ballester-Bolinches, A., Esteban-Romero, R. and Asaad, M., Products of Finite Groups (Walter De Gruyter, Berlin–New York, 2010).CrossRefGoogle Scholar
Bianchi, M., Brough, J. M. A., Camina, R. D. and Pacifici, E., ‘On vanishing class sizes in finite groups’, J. Algebra 489 (2017), 446–459.CrossRefGoogle Scholar
Brough, J., ‘On vanishing criteria that control finite group structure’, J. Algebra 458 (2016), 207–215.CrossRefGoogle Scholar
Brough, J. and Kong, Q., ‘On vanishing criteria that control finite group structure II’, Bull. Aust. Math. Soc. 98 (2018), 251–257.CrossRefGoogle Scholar
Cossey, J. and Wang, Y., ‘Remarks on the length of conjugacy classes of finite groups’, Comm. Algebra 29 (1999), 4347–4353.CrossRefGoogle Scholar
Doerk, K. and Hawkes, T. O., Finite Soluble Groups (Walter De Gruyter, Berlin–New York, 1992).CrossRefGoogle Scholar
Felipe, M. J., Martínez-Pastor, A. and Ortiz-Sotomayor, V., ‘Zeros of irreducible characters in factorised groups’, Ann. Mat. Pura Appl. (4) 198 (2019), 129–142.CrossRefGoogle Scholar
He, L., ‘Notes on non-vanishing elements of finite solvable groups’, Bull. Malays. Math. Sci. Soc. 35 (2012), 163–169.Google Scholar
Kong, Q. and Chen, S., ‘A note on conjugacy class sizes of vanishing elements in finite groups’, Asian-Eur. J. Math. 15(4) (2022), Article no. 2250067, 3 pages.CrossRefGoogle Scholar
Li, S., ‘Finite groups with exactly two class lengths of elements of prime power order’, Arch. Math. (Basel) 67(2) (1996), 100–105.Google Scholar