Actions with nilpotent fixed point subgroup

Abstract.

Let A and G be finite groups and suppose that A acts coprimely on G. Several results on the A-invariant character theory of G lead us to study those groups G having a unique A-invariant Sylow p-subgroup for every prime divisor p of |G|. In certain sense, the A-structure of these groups is similar to the structure of nilpotent groups.