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.
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机译：一个完整的组是一个琐碎的中心，内部具有所有同构。本文利用群同调性给出了一个满足C G （N）≤N的有限半直接乘积G = N rtimes H {G = N rtimes H}的充分条件，并证明了部分逆。这些结果足以完全表征完整的有限排列花环产品，并且对于有限标准花环产品而言，足以进行表征。
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