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International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
May 21-24, 2002
Vanderbilt University
Nashville, TN, USA

Organizers
Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote

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A constructing of finitely presented semigroups whith some exotic properties.
by
Alexei Kanel-Belov
Moscow Center of Continuous Mathematics Education
Coauthors: Ivanov Ilia (Moscow State University)

This talk is devoted a construction of finitely presented semigroups with some exotic properties.

The main result is as follows.

Theorem There exists a constant M such that if \alpha > M is a recursive real number (i.e. there is an algorithm for calculating each digit of its decimal presentation) then there exists a semigroup G such that GK(G)=\alpha.

The proof is based on a technique of Minsky machines (which was learned by one author from conversations with Mark Sapir).

Date received: December 30, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-27.