On finite and Abelian groups generated by finite automata
Andriy Russyev · Matematychni Studii · 2005
À. Â. Ðóññ¹â ÏÐÎ ÑÊIÍ×ÅÍÍI ÒÀ ÀÁÅËÅÂI ÃÐÓÏÈ, ÏÎÐÎÄÆÅÍI ÑÊIÍ×ÅÍÍÈÌÈ ÀÂÒÎÌÀÒÀÌÈ A. V. Russyev.On finite and Abelian groups generated by finite automata , Matematychni Studii, 24 (2005) 139146.We present a sufficient condition for finiteness of groups generated by a finite automaton.We provide a criterion when a group generated by a finite automaton over two-letter alphabet is Abelian.À. Â. Ðóññåâ.Î êîíå÷íûõ è àáåëåâûõ ãðóïïàõ, ïîðîæäåííûõ êîíå÷íûìè àâòîìàòàìè // Ìàòåìàòè÷íi Ñòóäi¨.2005.Ò.24, 2. C.139146.Ïðèâåäåíî äîñòàòî÷íîå óñëîâèå êîíå÷íîñòè ãðóïïû, ïîðîæäåííîé êîíå÷íûì àâòîìàòîì.Äàí êðèòåðèé àáåëåâîñòè ãðóïïû, ïîðîæäåííîé êîíå÷íûì àâòîìàòîì íàä äâóõýëåìåíòíûì àëôàâèòîì.