The paper deals with the solution of Shevrin ans Sapir problem. Infinite finitely presented nilsemigroup is constructed. The construction is based on aperiodic tilings, Goodman-Strauss type theorems on uniformly elliptic space. Space is called {\it uniformly elliptic} iff there is universal constant $\lambda>0$ such that any two points $A$ and $B$ on distant $D$ can be joined by family of geodesic lines generating a disc of wideness $\lambda\cdot D$. Research was supported by the grant RFBR N 14-01-00548

中文翻译：

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无限有限呈现Nilsemi群的构造

本文讨论了 Shevrin 和 Sapir 问题的解决方案。构造了无限有限呈现的 nilsemigroup。该构造基于均匀椭圆空间上的非周期性平铺、Goodman-Strauss 型定理。空间被称为 {\it 一致椭圆}，如果存在通用常数 $\lambda>0$，使得远处 $D$ 上的任何两个点 $A$ 和 $B$ 可以通过一系列测地线连接，产生一个宽的圆盘$\lambda\cdot D$。研究得到了 RFBR N 14-01-00548 的资助