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On conditional permutability and saturated formations

Part of: Representation theory of groups

Published online by Cambridge University Press:  30 March 2011

M. Arroyo-Jordá ,
P. Arroyo-Jordá  and
M. D. Pérez-Ramos
M. Arroyo-Jordá
Affiliation:
Escuela Técnica Superior de Ingenieros Industriales, Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain, ([email protected]; [email protected])
P. Arroyo-Jordá
Affiliation:
Escuela Técnica Superior de Ingenieros Industriales, Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain, ([email protected]; [email protected])
M. D. Pérez-Ramos
Affiliation:
Departament d'Àlgebra, Universitat de València, Calle del Doctor Moliner 50, 46100 Burjassot (València), Spain ([email protected])
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Abstract

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Two subgroups A and B of a group G are said to be totally completely conditionally permutable (tcc-permutable) in G if X permutes with Yg for some g ∊ 〈X, Y〉, for all X ≤ A and Y ≤ B. We study the belonging of a finite product of tcc-permutable subgroups to a saturated formation of soluble groups containing all finite supersoluble groups.

Keywords

finite groupsproducts of subgroupssaturated formationsconditional permutability

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D40: Products of subgroups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 309 - 319
Copyright
Copyright © Edinburgh Mathematical Society 2011

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