“…The first results for p-groups, nilpotent groups and groups with normal Sylow 2-subgroups are due (respectively) to D. Coleman [2], A. Saksonov [21], S. Jackowski and Z. Marciniak [16]. Further work by, among others, S. Sehgal, M. Parmenter, Y. Li [1], E. Jespers and M. Hertweck [13], M. Hertweck [11,12,9] and M. Hertweck and W. Kimmerle [14] enlarged the class of groups with a positive answer greatly. M. Mazur [19,20] showed that the question is closely related to the Isomorphism problem.…”