Abstract
thbirthday1. INTRODUCTORY REMARKSLet Gbe a group and denote by PAut G the group of power automor-phisms of G(see [4]). An automorphism of Gis called an I-automorphismof Gif it maps every infinite subgroup of Gonto itself. The set IAut Gof all I-automorphisms of Gis a normal subgroup of Aut G containingPAut G .IAut G has been investigated by Curzio et al. [5],where theyoften consider the case when IAut G =PAut G or at least IAut G isabelian.Here we consider the structural restriction on G when IAut G =PAut G . One of the major outcomes of this work is that for manygroups Hin fact IAut H= PAut H holds. We also characterize infiniteChernikov groups Gfor which IAut G = PAut G .
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