A note on finite PST-groups

Abstract. 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