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On Neumann’s BFC-theorem and finite-by-nilpotent profinite groups | ||
| International Journal of Group Theory | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 26 آبان 1401 اصل مقاله (418.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2022.134785.1802 | ||
| نویسنده | ||
| Wállef da Silva* | ||
| Department of Mathematics, University of Brasilia, Brasilia-DF, Brazil | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Conjucagy classes؛ verbal subgroups؛ profinite groups؛ FC-groups | ||
| مراجع | ||
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[17] P. Shumyatsky and W. da Silva, Engel conditions for soluble and pronilpotent groups, Advances in Group Theory and Applications, accepted for publication, (2022). [18] J. Wiegold, Groups with boundedly finite classes of conjugate elements, Proc. R. Soc. Lond., Ser. A, 238 (1957) 389–401. | ||
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