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Finite Soluble Groups with Permutable Subnormal Subgroups

✍ Scribed by Manuel J Alejandre; A Ballester-Bolinches; M.C Pedraza-Aguilera

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
139 KB
Volume
240
Category
Article
ISSN
0021-8693

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✦ Synopsis

A finite group G is said to be a PST -group if every subnormal subgroup of G permutes with every Sylow subgroup of G. We shall discuss the normal structure of soluble PST -groups, mainly defining a local version of this concept. A deep study of the local structure turns out to be crucial for obtaining information about the global property. Moreover, a new approach to soluble PT -groups, i.e., soluble groups in which permutability is a transitive relation, follows naturally from our vision of PSTgroups. Our techniques and results provide a unified point of view for T -groups, PT -groups, and PST -groups in the soluble universe, showing that the difference between these classes is quite simply their Sylow structure.

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