Author:
Oliynyk Andriy, ,Prokhorchuk Veronika,
Abstract
It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups GL(n,Z). The number of states of automorphisms that correspond to elementary matrices i computed. Using the representation of GL(2,Z) over an alphabet of size 4 a finite state representation of the freegroup of rank 2 over binary alphabet is constructed.
Publisher
Luhansk Taras Shevchenko National University
Subject
Discrete Mathematics and Combinatorics,Algebra and Number Theory
Reference17 articles.
1. [1] V. Prokhorchuk,On finite state automaton actions of HNN extensions offree abelian groups, Carpathian Math. Publ.,13, N. 1, 2021, pp. 180-188;DOI: 10.15330/cmp.13.1.180-188.
2. [2] A.S. Oliynyk,Finite state wreath powers of transformation semigroups, SemigroupForum,82, N. 3, 2011, pp. 423-436; DOI: 10.1007/s00233-011-9292-z.
3. [3] L. Kaloujnine,Sur lesp-groupes de Sylow du groupe sym ́etrique du degr ́epm,C. R. Acad. Sci. Paris,221, 1945, pp. 222-224.
4. [4] R.I. Grigorchuk, V.V. Nekrashevich and V.I. Sushchansky,Automata, dynamicalsystems, and groups, Tr. Mat. Inst. Steklova,231, 2000, pp. 134-214.
5. [5] V. Nekrashevych,Self-similar groups, Mathematical Surveys and Monographs,117, American Mathematical Society, Providence, RI, 2005, xii+231 p.;DOI: 10.1090/surv/117.