A. S. Oliinyk, V. I. Sushchanskiĭ, “The groups of <nobr>$ZC$</nobr>-automaton transformations”, Sibirsk. Mat. Zh., 2010, Volume 51, Number 5,Pages <nobr>1102

This article is cited in 1 paper

The groups of $ZC$-automaton transformations

A. S. Oliinyk^a, V. I. Sushchanskiĭ^b

^a Taras Shevchenko Kiev National University, Kiev, Ukraine
^b Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

Abstract: Under study are the $ZC$-automata and the transformation groups determined by them. We establish relationships between the group of $ZC$-automaton transformations and the group of infinite unitriangular integer matrices. We describe the derived series of the group of $ZC$-automaton transformations and present conditions for the representability of residually solvable groups by $ZC$-automaton transformations. We construct a continual family of $ZC$-automata with two states, each of which generates a free semigroup.

Keywords: automaton, automaton transformation, unitriangular matrix, residually solvable group, derived series, free semigroup.

UDC: 512.54

Received: 10.09.2009