ACTIONS WITH NILPOTENT FIXED-POINT SUBGROUP

Let A and G be finite groups and suppose that A acts coprimely on G. S everal results on the A-invariant character theory of G lead us to stu dy those groups G' having a unique A-invariant Sylow p-subgroup fcr ev ery prime divisor p of \G\. In certain sense, the A-structure of these groups is similar to the structure of nilpotent groups.