Residually finite finitely presented solvable groups
Olga Kharlampovich, Alexei Myasnikov, Mark Valentinovich Sapir · arXiv (Cornell University) · 2012
We construct the first examples of finitely presented residually finite groups with arbitrarily complicated word problem and depth function. The groups are solvable of class 3. We also prove that the universal theory of finite solvable of class 3 groups is undecidable, and give an example of a finitely presented (solvable of class 3) group with NP-complete word problem.