论文标题
线性不匹配的逐循环组是异步自动的
Linearly Mismatched Free-by-Cyclic Groups are Asynchronously Automatic
论文作者
论文摘要
我们称为自由循环组的家庭，定义为$ g = \ left <a，t，b_1，b_1，b_2，\ ldots b_k \ mid at = ta，b_1^{ - 1} tb_1 = a^a^a^{n_1} n_2，\ ldots n_k \ in \ mathbb z $线性不匹配，因为用于定义HNN扩展的自动形态以不同的速度线性生长。使用来自Elder论文的技术，即带有平行稳定字母结构的单词，我们证明线性不匹配的自由群体是异步自动的，因此它们具有可解决的单词问题。
We call the family of free-by-cyclic groups defined by $G = \left< a, t, b_1, b_2, \ldots b_k \mid at = ta, b_1^{-1}tb_1 = a^{n_1}t, \ldots b_k^{-1}tb_k = a^{n_k}t \right>$ for $n_1, n_2, \ldots n_k \in \mathbb Z$ linearly mismatched since the automorphisms used to define the HNN extensions grow linearly at different rates. Using techniques from Elder's thesis, namely words with a parallel stable letter structure, we prove that linearly mismatched free-by-cyclic groups are asynchronously automatic, and thus they have a solvable word problem.
