论文标题
基本团体的非标准开莉自动表示
Nonstandard Cayley automatic representations of fundamental groups
论文作者
论文摘要
我们构建了一个新的Cayley自动表示的新家族，$ \ Mathbb {Z}^n \ rtimes_a \ Mathbb {Z} $，而普通子组$ \ MATHBB {z}^n $都不是其环状组件的每个均可识别的autoMatemon Automate venite automatizable。对于$ n = 2 $，我们从$ \ mathrm {gl}（2，\ mathbb {z}）$中描述一个与这些表示相对应的矩阵。我们的动机是由这些群体的所有可能的Cayley自动表示的表征的问题。
We construct a new family of Cayley automatic representations of semidirect products $\mathbb{Z}^n \rtimes_A \mathbb{Z}$ for which none of the projections of the normal subgroup $\mathbb{Z}^n$ onto each of its cyclic components is finite automaton recognizable. For $n=2$ we describe a family of matrices from $\mathrm{GL}(2,\mathbb{Z})$ corresponding to these representations. We are motivated by a problem of characterization of all possible Cayley automatic representations of these groups.
