Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
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.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
1078-1082
Opis fizyczny
Daty
wydano
2013-06-01
online
2013-03-28
Twórcy
- Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain
autor
- Department of Mathematics, University of Kentucky, Lexington, KY, 40506-0027, USA
autor
autor
- 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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0222-z