Let $\{G_i :i\in\N\}$ be a family of finite Abelian groups. We say that a subgroup $G\leq \prod\limits_{i\in \N}G_i$ is \emph{order controllable} if for every $i\in \mathbb{N}$ there is $n_i\in \mathbb{N}$ such that for each $c\in G$, there exists $c_1\in G$ satisfying that $c_{1|[1,i]}=c_{|[1,i]}$, $supp (c_1)\subseteq [1,n_i]$, and order$(c_1)$ divides order$(c_{|[1,n_i]})$. In this paper we investigate the structure of order controllable group codes. It is proved that if $G$ is an order controllable, shift invariant, group code over a finite abelian group $H$, then $G$ possesses a finite canonical generating set. Furthermore, our construction also yields that $G$ is algebraically conjugate to a full group shift.

翻译：$G_i: i\ in\ n$@ $应该是一个限定的 Abelian 集团的家族。 我们说, 如果对于每$\ mathbb{ N} $有 $_i: i\ in\\ n$ $, 那么对于每$ $: i_ i_ $ i_ i\ 美元, $ c_ 1\ g$, 满足于$1\ ⁇ { i] { c[1]} $, $supp (c_ 1)\ subseteq [1_ i] $, 并且订购 $ (c_ 1) 命令可以控制 $ 。 在本文中, 我们调查了命令控制组码的结构。 证明, 如果$G$是可控制的命令, 变换的, 集团对一个限定的 $H $, 然后$G$$ 拥有一个固定的 Canticalcalgal 组合。 此外, 我们的建筑产量也是制成的。