6533b7dbfe1ef96bd126fc2d

RESEARCH PRODUCT

A note on finite PST-groups

Adolfo Ballester BolinchesRamón Esteban RomeroMatthew F. Ragland

subject

Transitive normalityGrups Teoria deÀlgebraFinite groupMATEMATICA APLICADASylow-permutable subgroup

description

[EN] A finite group G is said to be a PST-group if, for subgroups H and K of G with H Sylow-permutable in K and K Sylow-permutable in G, it is always the case that H is Sylow-permutable in G. A group G is a T*-group if, for subgroups H and K of G with H normal in K and K normal in G, it is always the case that H is Sylow-permutable in G. In this paper, we show that finite PST-groups and finite T*-groups are one and the same. A new characterisation of soluble PST-groups is also presented.

10.1515/jgt.2007.016http://dx.doi.org/10.1515/JGT.2007.016