Maximal subgroups and PST-groups

• Autorzy: Adolfo Ballester-Bolinches , James Beidleman , Ramón Esteban-Romero , Vicent Pérez-Calabuig
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, π -length, ranks
• 20E28: Maximal subgroups
• 20E15: Chains and lattices of subgroups, subnormal subgroups
• 20F16: Solvable groups, supersolvable groups
• 20D05: Finite simple groups and their classification

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 6
• Strony: 1078-1082

Daty

wydano

2013-06-01

online

2013-03-28

Twórcy

autor

Adolfo Ballester-Bolinches

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

autor

James Beidleman

• Department of Mathematics, University of Kentucky, Lexington, KY, 40506-0027, USA

autor

Ramón Esteban-Romero

autor

Vicent Pérez-Calabuig

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

Bibliografia

• [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/10.1515/9783110220612[Crossref]
• [2] Ballester-Bolinches A., Ezquerro L.M., Classes of Finite Groups, Math. Appl. (Springer), 584, Springer, Dordrecht, 2006
• [3] Doerk K., Hawkes T., Finite Soluble Groups, de Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992 http://dx.doi.org/10.1515/9783110870138[Crossref]
• [4] Gaschütz W., Über die Ø-Untergruppe endlicher Gruppen, Math. Z., 1953, 58, 160–170 http://dx.doi.org/10.1007/BF01174137[Crossref]
• [5] Huppert B., Endliche Gruppen I, Grundlehren Math. Wiss., 134, Springer, Berlin, Berlin-New York, 1967 http://dx.doi.org/10.1007/978-3-642-64981-3[Crossref]
• [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/s00013-010-0207-0[WoS][Crossref]

Identyfikatory

DOI

10.2478/s11533-013-0222-z