Laurent Bartholdi, Illya I. Reznykov
Published 2005-06-10, updated 2007-01-12Version 2
We consider a very simple Mealy machine (three states over a two-symbol alphabet), and derive some properties of the semigroup it generates. In particular, this is an infinite, finitely generated semigroup; we show that the growth function of its balls behaves asymptotically like n^2.4401..., where this constant is 1 + log(2)/log((1+sqrt(5))/2); that the semigroup satisfies the identity g^6=g^4; and that its lattice of two-sided ideals is a chain.
Comments: 20 pages, 1 diagram
Journal: Internat. J. Algebra Comput. 18 (2008), no. 1, 59--82
Properness of nilprogressions and the persistence of polynomial growth of given degree
On the structure of groups with polynomial growth III
Polynomial growth and subgroups of $\mathrm{Out}(F_{\tt n})$
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