AbstarctLet γn = [x1,…,xn] be the nth lower central word. Denote by Xn the set of γn -values in a group G and suppose that there is a number m such that $|{g^{{X_n}}}| \le m$ for each g ∈ G. We prove that γn+1(G) has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.

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关于有限幂群

摘要γn= [X1,…,Xn] 成为n较低的中心词。表示为Xn的集合γn- 组中的值G并假设有一个数字米这样$|{g^{{X_n}}}| \le m$对于每个G∈G. 我们证明γn+1(G)有有限（米，n) - 有界顺序。这推广了广为人知的 BH Neumann 定理，即 BFC 群的交换子群是有限的。