Unsolvable Problems in Groups With Solvable Word Problem
Unsolvable Problems in Groups With Solvable Word Problem
复制标题
具有可解决文字问题的小组中无法解决的问题
DOI：
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
J. McCool
中科院分区：
文献类型：
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作者：
J. McCool
设G是一个具有可解字问题的群.我们有兴趣问一下，对于这样的群体来说，还有哪些其他决策问题一定是可以解决的。因此，很容易看出，存在有效的程序来确定这样的群是否平凡，或给定类的幂零。另一方面，对于这样的群，共轭问题不一定是可解的，因为Fridman [5]已经证明，对于Novikov [9]给出的具有不可解共轭问题的群，字问题是可解的。
Let G be a finitely presented group with solvable word problem. It is of some interest to ask which other decision problems must necessarily be solvable for such a group. Thus it is easy to see that there exist effective procedures to determine whether or not such a group is trivial, or nilpotent of a given class. On the other hand, the conjugacy problem need not be solvable for such a group, for Fridman [5] has shown that the word problem is solvable for the group with unsolvable conjugacy problem given by Novikov [9].