Viewing Dehn's algorithm as a rewriting system, we generalize to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to include finitely generated nilpotent groups, many relatively hyperbolic groups including geometrically finite groups and fundamental groups of certain geometrically decomposable 3-manifolds. The class has several nice closure properties. We also show that if a group has an infinite subgroup and one of exponential growth, and they commute, then it does not admit such an algorithm. We dub these Cannon's algorithms.

中文翻译：

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关于 DEHN 算法的一般化

将 Dehn 的算法视为重写系统，我们推广到允许包含不一定代表组元素的字母的字母表。这扩展了算法解决单词问题的群类别，以包括有限生成的幂零群、许多相对双曲群，包括几何有限群和某些几何可分解 3 流形的基本群。该类有几个不错的闭包属性。我们还表明，如果一个群有一个无限子群和一个指数增长的子群，并且它们是通勤的，那么它就不会接受这样的算法。我们将这些 Cannon 算法称为。