论文标题
障碍物的障碍物将定理嵌入具有可解决单词问题的残留有限的群体
Obstruction to a Higman embedding theorem for residually finite groups with solvable word problem
论文作者
论文摘要
我们证明，对于有限生成的剩余群体，具有可解决的单词问题是不足以成为有限呈现的残留组的子组的足够条件。障碍物是由一个有限有限的单词问题给出的障碍，没有有效的方法可以在某些非身份元素上找到对该元素具有非平凡图像的有限群的形态。我们还证明，该组的深度功能比任何递归函数都要快。
We prove that, for a finitely generated residually finite group, having solvable word problem is not a sufficient condition to be a subgroup of a finitely presented residually finite group. The obstruction is given by a residually finite group with solvable word problem for which there is no effective method that allows, given some non-identity element, to find a morphism onto a finite group in which this element has a non-trivial image. We also prove that the depth function of this group grows faster than any recursive function.
