JournalsggdVol. 14, No. 2pp. 567–589

Lamplighter groups, bireversible automata, and rational series over finite rings

  • Rachel Skipper

    The Ohio State University, Columbus, USA
  • Benjamin Steinberg

    City College of New York, USA
Lamplighter groups, bireversible automata, and rational series over finite rings cover
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Abstract

We realize lamplighter groups AZA\wr \mathbb Z, with AA a finite abelian group, as automaton groups via affine transformations of power series rings with coefficients in a finite commutative ring. Our methods can realize AZA\wr \mathbb Z as a bireversible automaton group if and only if the 2-Sylow subgroup of AA has no multiplicity one summands in its expression as a direct sum of cyclic groups of order a power of 2.

Cite this article

Rachel Skipper, Benjamin Steinberg, Lamplighter groups, bireversible automata, and rational series over finite rings. Groups Geom. Dyn. 14 (2020), no. 2, pp. 567–589

DOI 10.4171/GGD/555