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Some classes of finite groups and mutually permutable products

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Some classes of finite groups and mutually permutable products

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Asaad, M.; Ballester-Bolinches, Adolfo; Beidleman, J.C.; Esteban Romero, Ramón

Aquest document és un/a article, creat/da en: 2008

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 a converse of Lagrange¿s theorem) and SC-groups (groups whose chief factors are simple) are SC-groups, by means of a local version. Next we show that the product of pairwise mutually permutable Y-groups is supersoluble. Finally, we give a local version of the result stating that when 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.

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