A note on finite PST-groups

This paper has been published in Journal of Group Theory, 10(2):205-210 (2007). Copyright 2007 by Walter de Gruyter. The final publication is available at www.degruyter.com. http://dx.doi.org/10.1515/JGT.2007.016 http://www.degruyter.com/view/j/jgth.2007.10.issue-2/jgt.2007.016/jgt.2007.016.xml[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.Supported by Grant MTM2004-08219-C02-02 from Ministerio de Educación y Ciencia (Spain) and FEDER (European Union).Ballester Bolinches, A.; Esteban Romero, R.; Ragland, MF. (2007). A note on finite PST-groups. Journal of Group Theory. 2(10). doi:10.1515/JGT.2007.01621