Construction of infinite finitely presented nilsemigroup (short version)

TL;DR

This paper presents a construction of an infinite finitely presented nilsemigroup with the identity x^9=0, addressing a longstanding problem in algebra and demonstrating a novel example of such algebraic structures.

Contribution

It provides the first known construction of an infinite finitely presented nilsemigroup with a specific nilpotency identity, solving a problem posed by Shevrin and Sapir.

Findings

Construction of an infinite finitely presented nilsemigroup with x^9=0

Addresses a problem posed by Shevrin and Sapir

Advances understanding of finitely presented nilsemigroups

Abstract

This paper is devoted to construction of finitely presented infinite nil semigroup with identity $x^9=0$. This construction answers to the problem of Lev Shevrin and Mark Sapir. This is the short version of the paper presenting the main ideas of the construction. The work was carried out with the help of the Russian Science Foundation Grant N 17-11-01377. The first author is the winner of the contest Young Mathematics of Russia .