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The Constraction of Finitely-Defined semigroups, satisfying some exotic properties
by
I.A. Ivanov
The following examples of semigroups, groups and rings with kit of characteristics which course were considered exotic are well-known. Namely, semigroups with non-integer Gelfand-Kirillov dimentionality, non-nilpotent nil-semigroups and nil-rings, finitely-defined infinite periodic groups, and others.
Theorem. There exists the finitely-determined semigroups: G1, G2, G3, such as: a) The Gelfand-Kirillov dimentionality for G1 - is not integer; b) And more, for any large enouth recursive number \alpha which has an algorithm of determine all its decimal digits, there exists a semigroup G2 with Gelfand-Kirillov dimentionality equal \alpha. c) Growth function in G3 VG3(n) = c·ln n ·nk, there V(n) is number of various words with length n.
Date received: November 14, 2000
Copyright © 2000 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 # cafo-20.