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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 11, Issue 6 (Jun 2013)


Maximal subgroups and PST-groups

Adolfo Ballester-Bolinches / James Beidleman / Ramón Esteban-Romero
  • Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain
  • Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022, València, Spain
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/ Vicent Pérez-Calabuig
Published Online: 2013-03-28 | DOI: https://doi.org/10.2478/s11533-013-0222-z


A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions of Kaplan’s results, which enables a better understanding of the relationships between these classes.

MSC: 20D05; 20D10; 20E15; 20E28; 20F16

Keywords: Finite groups; Permutability; Sylow-permutability; Maximal subgroups; Supersolubility

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About the article

Published Online: 2013-03-28

Published in Print: 2013-06-01

Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0222-z.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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