论文标题
关于某些口头亚组的有限属性
On finiteness of some verbal subgroups in profinite groups
论文作者
论文摘要
给定一个组单词$ w $和一个$ g $，$ g $中的$ w $值的集合用$ g_w $表示，而口头子组$ w（g）$是$ g_w $生成的。在本文中，我们考虑pribinite群体承认一个$ w $，以便$ g_w $的基数小于$ 2^{\ aleph_0} $，而$ w（g）$是由有限的许多$ w $ values生成的。对于几个单词家庭$ w $，我们表明，在这些假设下，$ W（g）$必须是有限的。我们的结果与群体单词的简洁性概念有关。
Given a group word $w$ and a group $G$, the set of $w$-values in $G$ is denoted by $G_w$ and the verbal subgroup $w(G)$ is the one generated by $G_w$. In the present paper we consider profinite groups admitting a word $w$ such that the cardinality of $G_w$ is less than $2^{\aleph_0}$ and $w(G)$ is generated by finitely many $w$-values. For several families of words $w$ we show that under these assumptions $w(G)$ must be finite. Our results are related to the concept of conciseness of group words.
