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SOME PRODUCTS OF SUBGROUPS AND VANISHING CONJUGACY CLASS SIZES

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

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