# On Neumann’s BFC-theorem and finite-by-nilpotent profinite groups

Document Type : Research Paper

Author

Department of Mathematics, University of Brasilia, Brasilia-DF, Brazil

10.22108/ijgt.2022.134785.1802

Abstract

Let $\gamma_{n}=[x_{1},\ldots,x_{n}]$ be the $n$th lower central word and $X_{n}(G)$ the set of $\gamma_{n}$-values in a group $G$. Suppose that $G$ is a profinite group where, for each $g\in G$, there exists a positive integer $n=n(g)$ such that the set $g^{X_{n}(G)}=\{g^{y}\,|\,y\in X_{n}(G)\}$ contains less than $2^{\aleph_{0}}$ elements. We prove that $G$ is a finite-by-nilpotent group.

Keywords

Main Subjects

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