论文标题
有限生成的组有限商的可计算性
Computability of finite quotients of finitely generated groups
论文作者
论文摘要
我们系统地研究其明显有限的商构成递归集的组。我们给出了几个定义，并证明了这类群体的基本属性，尤其是强调了深度函数的增长与单词问题的可溶性之间的联系。我们提供了无限介绍的群体的例子，他们的有限商可以有效地列举。最后，我们的主要结果是，剩余的群体甚至可以递归地呈现，并且仍然具有可计算的有限商，另一方面，它可以有可解决的单词问题，而仍然没有可计算的有限商。
We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth function and solvability of the word problem. We give examples of infinitely presented groups whose finite quotients can be effectively enumerated. Finally, our main result is that a residually finite group can be even not recursively presented and still have computable finite quotients, and that, on the other hand, it can have solvable word problem while still not having computable finite quotients.
