ON A CLASS OF AUTOMATA GROUPS GENERALIZING LAMPLIGHTER GROUPS-Reference-Cited by-同舟云学术

ON A CLASS OF AUTOMATA GROUPS GENERALIZING LAMPLIGHTER GROUPS

Published:2005-10 Issue:05n06 Volume:15 Page:1213-1234
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

SILVA P. V.¹,STEINBERG B.²

Affiliation:

1. Departamento de Matemática Pura, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

2. School of Mathematics and Statistics, Carleton University, 1125 Colonel by Drive, Ottawa, Ontario K1S 5B6, Canada

Abstract

We study automata groups generated by reset automata. Every lamplighter group ℤ/nℤ wr ℤ can be generated by such an automaton, and in general these automata groups are similar in nature to lamplighters: they are amenable locally-finite-by-cyclic groups; under mild decidable conditions, the semigroups generated by such automata are free. Parabolic subgroups and fractal properties are considered.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196705002761

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