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Open Mathematics

formerly Central European Journal of Mathematics

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

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IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

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2391-5455
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Volume 11, Issue 6 (Jun 2013)

Issues

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

Abstract

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

  • [1] Ballester-Bolinches A., Esteban-Romero R., Asaad M., Products of Finite Groups, de Gruyter Exp. Math., 53, Walter de Gruyter, Berlin, 2010 http://dx.doi.org/10.1515/9783110220612CrossrefGoogle Scholar

  • [2] Ballester-Bolinches A., Ezquerro L.M., Classes of Finite Groups, Math. Appl. (Springer), 584, Springer, Dordrecht, 2006 Google Scholar

  • [3] Doerk K., Hawkes T., Finite Soluble Groups, de Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992 http://dx.doi.org/10.1515/9783110870138CrossrefGoogle Scholar

  • [4] Gaschütz W., Über die Ø-Untergruppe endlicher Gruppen, Math. Z., 1953, 58, 160–170 http://dx.doi.org/10.1007/BF01174137CrossrefGoogle Scholar

  • [5] Huppert B., Endliche Gruppen I, Grundlehren Math. Wiss., 134, Springer, Berlin, Berlin-New York, 1967 http://dx.doi.org/10.1007/978-3-642-64981-3CrossrefGoogle Scholar

  • [6] Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25 http://dx.doi.org/10.1007/s00013-010-0207-0Web of ScienceCrossrefGoogle Scholar

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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