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- W2996750177 abstract "Let $gamma_n=[x_1,ldots,x_n]$ be the $n$th lower central word. Suppose that $G$ is a profinite group where the conjugacy classes $x^{gamma_n(G)}$ contains less than $2^{aleph_0}$ elements for any $x in G$. We prove that then $gamma_{n+1}(G)$ has finite order. This generalizes the much celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite. Moreover, it implies that a profinite group $G$ is finite-by-nilpotent if and only if there is a positive integer $n$ such that $x^{gamma_n(G)}$ contains less than $2^{aleph_0}$ elements, for any $xin G$." @default.
- W2996750177 created "2019-12-26" @default.
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- W2996750177 date "2020-12-01" @default.
- W2996750177 modified "2023-09-26" @default.
- W2996750177 title "On finite-by-nilpotent profinite groups" @default.
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- W2996750177 doi "https://doi.org/10.22108/ijgt.2019.119581.1577" @default.
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