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, but the depth function of which grows faster than any recursive function.

中文翻译：

---

具有可解词问题的残差有限群的希格曼嵌入定理的障碍

我们证明，对于有限生成的残差有限群，具有可解的词问题并不是成为有限表示的残差有限群的子群的充分条件。障碍由具有可解词问题的残差有限群给出，但其深度函数的增长速度比任何递归函数都快。