Testing of subgroups of a finite group for some embedding properties like pronormality

Here we describe algorithms for testing subgroups of a finite group for the following embedding properties: pronormality, abnormality, paranormality, and their weak analogs. The method is based on the decomposition of the main group into some double cosets. These algorithms are realized in the computer algebra system GAP. ©1999 Kluwer Academic/Plenum Publishers.