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RESEARCH PRODUCT
Finite Soluble Groups with Permutable Subnormal Subgroups
Adolfo Ballester-bolinchesManuel J. AlejandreM. C. Pedraza-aguilerasubject
Discrete mathematicsSubnormal subgroupCombinatoricsComplement (group theory)Finite groupAlgebra and Number TheoryGroup (mathematics)Locally finite groupSylow theoremsComponent (group theory)Permutable primeMathematicsdescription
Abstract 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 PST -groups. 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-06-01 | Journal of Algebra |