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Algebra and Discrete Mathematics, 2009, Issue 4, Pages 10–17 (Mi adm140)  
This article is cited in 1 scientific paper (total in 1 paper)

SURVEY ARTICLE

A characterization via graphs of the soluble groups in which permutability is transitive

A. Ballester-Bolinchesa, John Cosseyb, R. Esteban-Romeroc

a Departament d'Algebra, Universitat de València, Dr. Moliner, 50, E–46100 Burjassot, València, Spain
b Mathematics Department, Mathematical Sciences Institute, Australian National University; Canberra, ACT 0200, Australia
c Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València; Camì de Vera, s/n; E–46022 València, Spain
Full-text PDF (217 kB) Citations (1)
Abstract: There are different ways to associate to a group a certain graph. In this context, it is interesting to ask for the relations between the structure of the group, given in group-theoretical terms, and the structure of the graphs, given in the language of graph theory.
In this paper we recall some properties of the groups in which permutability is a transitive relation and present a new characterisation of the class of soluble groups in which permutability is a transitive relation in graph-theoretical terms.
Keywords: Finite soluble group; PT-group; permutable subgroup; complete graph.
Received: 28.07.2009
Revised: 28.07.2009
Bibliographic databases:
Document Type: Article
MSC: 20D10, 05C25
Language: English
Citation: A. Ballester-Bolinches, John Cossey, R. Esteban-Romero, “A characterization via graphs of the soluble groups in which permutability is transitive”, Algebra Discrete Math., 2009, no. 4, 10–17
Citation in format AMSBIB
\Bibitem{BalCosEst09}
\by A.~Ballester-Bolinches, John~Cossey, R.~Esteban-Romero
\paper A characterization via graphs of the soluble groups in which permutability is transitive
\jour Algebra Discrete Math.
\yr 2009
\issue 4
\pages 10--17
\mathnet{http://mi.mathnet.ru/adm140}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2681479}
\zmath{https://zbmath.org/?q=an:1199.20028}
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