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FINITE TRIFACTORISED GROUPS AND $\unicode[STIX]{x1D70B}$-DECOMPOSABILITY

Part of: Representation theory of groups

Published online by Cambridge University Press:  31 January 2018

L. S. KAZARIN ,
A. MARTÍNEZ-PASTOR Open the ORCID record for A. MARTÍNEZ-PASTOR [Opens in a new window]  and
M. D. PÉREZ-RAMOS Open the ORCID record for M. D. PÉREZ-RAMOS [Opens in a new window]
L. S. KAZARIN
Affiliation:
Department of Mathematics, Yaroslavl P. Demidov State University, Sovetskaya Str. 14, 150003 Yaroslavl, Russia email [email protected]
A. MARTÍNEZ-PASTOR*
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada IUMPA-UPV, Universitat Politècnica de València, Camino de Vera, s/n, 46022 València, Spain email [email protected]
M. D. PÉREZ-RAMOS
Affiliation:
Departament de Matemàtiques, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain email [email protected]
*
✉[email protected]
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Abstract

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We derive some structural properties of a trifactorised finite group $G=AB=AC=BC$, where $A$, $B$, and $C$ are subgroups of $G$, provided that $A=A_{\unicode[STIX]{x1D70B}}\times A_{\unicode[STIX]{x1D70B}^{\prime }}$ and $B=B_{\unicode[STIX]{x1D70B}}\times B_{\unicode[STIX]{x1D70B}^{\prime }}$ are $\unicode[STIX]{x1D70B}$-decomposable groups, for a set of primes $\unicode[STIX]{x1D70B}$.

Keywords

finite groupsproducts of subgroups𝜋-decomposable groups𝜋-structure

MSC classification

Primary: 20D40: Products of subgroups
Secondary: 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 2 , April 2018 , pp. 218 - 228
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author was supported by Project VIP-008 of Yaroslavl P. Demidov State University and by a research grant from the Universitat de València as research visitor (Programa Propi d’Ajudes a la Investigació de la Universitat de València, Subprograma d’Atracció de Talent de VLC-Campus, Estades d’investigadors convidats (2017)). The second and third authors were supported by Proyecto MTM2014-54707-C3-1-P, Ministerio de Economía y Competitividad, Spain.

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