论文标题
关于言语亚组的有限
On finiteness of verbal subgroups
论文作者
论文摘要
给定一个gyp $ w $的集体字$ w $和一个$ w $ g $的集体$ g $，$ g_w $表示$ g $，而口头子组$ w（g）$是由$ g_w $生成的。如果$ w（g）$对于所有$ g $有限的$ w（g）$在其中$ w $是有限的，则“ $ w $”一词是简洁的。我们获得了几个结果，以支持以下猜想：每当$ u_1，\ dots，u_s $都是非交换器时，$ [u_1，\ dots，u_s] $的词都是简洁的。
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 $G_w$. The word $w$ is concise if $w(G)$ is finite for all groups $G$ in which $G_w$ is finite. We obtain several results supporting the conjecture that the word $[u_1,\dots,u_s]$ is concise whenever the words $u_1,\dots,u_s$ are non-commutator.
