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\(\mathfrak {Z}\)-permutable subgroups of finite groups

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Abstract

Let \(\mathfrak {Z}\) be a complete set of Sylow subgroups of a finite group \(G\), that is, a set composed of a Sylow \(p\)-subgroup of \(G\) for each \(p\) dividing the order of \(G\). A subgroup \(H\) of \(G\) is called \(\mathfrak {Z}\)-permutable if \(H\) permutes with all members of \(\mathfrak {Z}\). The main goal of this paper is to study the embedding of the \(\mathfrak {Z}\)-permutable subgroups and the influence of \(\mathfrak {Z}\)-permutability on the group structure.

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Acknowledgments

This Project was funded by the Deanship of Scientific Research (DSR), at King Abdulaziz University, Jeddah, under grant no. (1/31/RG). The authors, therefore, acknowledge with thanks DSR technical and financial support. The second and the third author have been supported by the research project MTM2010-19938-C03-01 from the Ministerio de Ciencia e Innovación, Spain, and the second author has also been supported by the National Natural Science Foundation of China (Grant No. 11271085). We also thank E. Vdovin for providing us with a proof of Theorem 9.

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Author notes

  1. R. Esteban-Romero

    Present address: Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    A. A. Heliel & M. O. Almestady

  2. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt

    A. A. Heliel

  3. Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain

    A. Ballester-Bolinches

  4. Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022, Valencia, Spain

    R. Esteban-Romero

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  1. A. A. Heliel
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  2. A. Ballester-Bolinches
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  3. R. Esteban-Romero
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  4. M. O. Almestady
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Correspondence to A. Ballester-Bolinches.

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Communicated by A. Constantin.

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Heliel, A.A., Ballester-Bolinches, A., Esteban-Romero, R. et al. \(\mathfrak {Z}\)-permutable subgroups of finite groups. Monatsh Math 179, 523–534 (2016). https://doi.org/10.1007/s00605-015-0756-1

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