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Transitivity of Sylow permutability, the converse of Lagrange's theorem, and mutually permutable products

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Transitivity of Sylow permutability, the converse of Lagrange's theorem, and mutually permutable products

dc.contributor.author	Asaad, M.
dc.contributor.author	Ballester-Bolinches, Adolfo
dc.contributor.author	Beidleman, J.C.
dc.contributor.author	Esteban Romero, Ramón
dc.date.accessioned	2016-01-07T09:27:39Z
dc.date.available	2016-01-07T09:27:39Z
dc.date.issued	2008
dc.identifier.uri	http://hdl.handle.net/10550/49788
dc.description.abstract	This paper is devoted to the study of mutually permutable products of finite groups. A factorised group G = AB is said to be a mutually permutable product of its factors A and B when each factor permutes with every subgroup of the other factor. We prove that mutually permutable products of Y -groups (groups satisfying the converse of Lagrange's theorem) and SC-groups (groups whose chief factors are simple) are SC -groups. Next, we show that a product of pairwise mutually permutable Y -groups is supersoluble. Finally, we give a local version of the result stating that if a mutually permutable product of two groups is a PST - group (that is, a group in which every subnormal subgroup permutes with all Sylow subgroups), then both factors are PST -groups
dc.language.iso	eng
dc.relation.ispartof	Trudy Instituta Matematiki, 2008, vol. 16, num. 1, p. 4-8
dc.rights.uri	info:eu-repo/semantics/openAccess
dc.source	Asaad, M. Ballester-Bolinches, Adolfo Beidleman, J.C. Esteban Romero, Ramón 2008 Transitivity of Sylow permutability, the converse of Lagrange's theorem, and mutually permutable products Trudy Instituta Matematiki 16 1 4 8
dc.subject	Àlgebra
dc.subject	Grups, Teoria de
dc.title	Transitivity of Sylow permutability, the converse of Lagrange's theorem, and mutually permutable products
dc.type	info:eu-repo/semantics/article
dc.date.updated	2016-01-07T09:27:39Z
dc.identifier.doi	http://mi.mathnet.ru/timb47
dc.identifier.idgrec	109035