Complete finite semidirect products and wreath products

A complete group is one with a trivial center and with all automorphisms inner. This paper uses group cohomology to give a sufficient condition for a finite semidirect product G = N rtimes H{G = N rtimes H} with C _G (N) ≤ N to be complete and proves a partial converse. These results are enough to fully characterize complete finite permutational wreath products and to specialize that characterization in the case of finite standard wreath products.