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Representations of a free group of rank two by time-varying Mealy automata

Adam Woryna (2005)

Discussiones Mathematicae - General Algebra and Applications

In the group theory various representations of free groups are used. A representation of a free group of rank two by the so-calledtime-varying Mealy automata over the changing alphabet is given. Two different constructions of such automata are presented.

R-trees and the Bieri-Neumann-Strebel invariant.

Gilbert Levitt (1994)

Publicacions Matemàtiques

Let G be a finitely generated group. We give a new characterization of its Bieri-Neumann-Strebel invariant Σ(G), in terms of geometric abelian actions on R-trees. We provide a proof of Brown's characterization of Σ(G) by exceptional abelian actions of G, using geometric methods.

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