Mixing times for Markov chains on wreath products and related homogeneous spaces.
Originally, m-independence, ℳ -rank, m-stability and m-normality were defined only for small stable theories. Here we extend the definitions to an arbitrary small countable complete theory. Then we investigate these notions in the new, broader context. As a consequence we show that any superstable theory with countable models is m-normal. In particular, any *-algebraic group interpretable in such a theory is abelian-by-finite.
In questo lavoro sono contenuti alcuni risultati riguardanti la struttura dei gruppi non-periodici in cui sottogruppi verificano opportune condizioni di modularità.
We show that the class of groups which have monoid presentations by means of finite special -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.
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.
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.
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.