Algorithms for permutability in finite groups

In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.This work has been supported by the grant MTM2010-19938-C03-01 (Ministerio de Ciencia e Innovacion, Spain). The first author has also been supported by a project of the National Natural Science Foundation of China (11271085). The third author has been supported by the predoctoral grant AP2010-2764 (Programa FPU, Ministerio de Educacion, Spain).Adolfo Ballester-Bolinches; Cosme-Llópez, E.; Esteban Romero, R. (2013). Algorithms for permutability in finite groups. Central European Journal of Mathematics. 11(11):1914-1922. doi:10.2478/s11533-013-0299-4S19141922111