Let G be a permutation group of a set Ω and k be a positive integer. The k-closure of G is the greatest (w.r.t. inclusion) subgroup G^(k) in Sym(Ω) which has the same orbits as has G under the componentwise action on the set Ω^k. It is proved that the k-closure of a finite nilpotent group coincides with the direct product of k-closures of all of its Sylow subgroups.

中文翻译：

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有限幂零置换群的 k-闭包结构

设G是一个集合 Ω 的置换群，k是一个正整数。G的k-闭包是Sym(Ω) 中最大的（wrt 包含）子群G ^{( k )}，它与G在集合 Ω ^k上的分量作用下具有相同的轨道。它证明了ķ用的直接产物的有限幂零群重合-closure K-其所有Sylow子群中的封闭件。