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Monoid presentations of groups by finite special string-rewriting systems

Duncan W. Parkes, V. Yu. Shavrukov, Richard M. Thomas (2010)

RAIRO - Theoretical Informatics and Applications

We show that the class of groups which have monoid presentations by means of finite special [λ]-confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.

Monoid rings that are firs.

Andreu Pitarch (1990)

Publicacions Matemàtiques

It is well known that the monoid ring of the free product of a free group and a free monoid over a skew field is a fir. We give a proof of this fact that is more direct than the proof in the literature.

Moyennabilité intérieure et extensions HNN

Yves Stalder (2006)

Annales de l’institut Fourier

On présente des conditions suffisantes pour qu’une extension HNN soit intérieurement moyennable, respectivement CCI, qui donnent des critères nécessaires et suffisants parmi les groupes de Baumslag-Solitar. On en déduit qu’un tel groupe, vu comme groupe d’automorphismes de son arbre de Bass-Serre, possède des éléments non triviaux qui fixent des sous-arbres non bornés.

Non-abelian group structure on the Urysohn universal space

Michal Doucha (2015)

Fundamenta Mathematicae

We prove that there exists a non-abelian group structure on the Urysohn universal metric space. More precisely, we introduce a variant of the Graev metric that enables us to construct a free group with countably many generators equipped with a two-sided invariant metric that is isometric to the rational Urysohn space. We list several related open problems.

On a formula for the asymptotic dimension of free products

G. C. Bell, A. N. Dranishnikov, J. E. Keesling (2004)

Fundamenta Mathematicae

We prove an exact formula for the asymptotic dimension (asdim) of a free product. Our main theorem states that if A and B are finitely generated groups with asdim A = n and asdim B ≤ n, then asdim (A*B) = max n,1.

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