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The \(D_{\pi }\)-property on products of \(\pi \)-decomposable groups

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The aim of this paper is to prove the following result: Let \(\pi \) be a set of odd primes. If the group \(G=AB\) is the product of two \(\pi \)-decomposable subgroups \(A=A_\pi \times A_{\pi '}\) and \(B=B_\pi \times B_{\pi '}\), then G has a unique conjugacy class of Hall \(\pi \)-subgroups, and any \(\pi \)-subgroup is contained in a Hall \(\pi \)-subgroup (i.e. G satisfies property \(D_{\pi }\)).

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Acknowledgements

We thank the reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Yaroslavl P. Demidov State University, Sovetskaya Str 14, 150014, Yaroslavl, Russia

    L. S. Kazarin

  2. Instituto Universitario de Matemática Pura y Aplicada (IUMPA-UPV), Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain

    A. Martínez-Pastor

  3. Departament de Matemàtiques, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot, (Valéncia), Spain

    M. D. Pérez-Ramos

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  1. L. S. Kazarin
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  2. A. Martínez-Pastor
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  3. M. D. Pérez-Ramos
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Correspondence to A. Martínez-Pastor.

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Research supported by Proyectos PROMETEO/2017/057 from the Generalitat Valenciana (Valencian Community, Spain), and PGC2018-096872-B-I00 from the Ministerio de Ciencia, Innovación y Universidades, Spain, and FEDER, European Union; and second author also by Project VIP-008 of Yaroslavl P. Demidov State University.

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Kazarin, L.S., Martínez-Pastor, A. & Pérez-Ramos, M.D. The \(D_{\pi }\)-property on products of \(\pi \)-decomposable groups. RACSAM 115, 13 (2021). https://doi.org/10.1007/s13398-020-00950-z

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  • DOI: https://doi.org/10.1007/s13398-020-00950-z

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