Abstract :
This paper discusses general properties of intrinsic isotropy subgroups of finite groups, a notion recently introduced by the author, and motivated by the relevance of such subgroups in problems of bifurcation with symmetry. The main results established here are that groups are or are not intrinsic isotropy subgroups of themselves depending only upon their order being odd or even, and the characterization of 2-nilpotent groups as an optimal class of groups having a unique maximal intrinsic isotropy subgroup. The simplest case when uniqueness is lost is shown to correspond to groups whose structure generalizes that of image4
