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Ultracompanions of subsets of a group

I. Protasov, S. Slobodianiuk (2014)

Commentationes Mathematicae Universitatis Carolinae

Let G be a group, β G be the Stone-Čech compactification of G endowed with the structure of a right topological semigroup and G * = β G G . Given any subset A of G and p G * , we define the p -companion Δ p ( A ) = A * G p of A , and characterize the subsets with finite and discrete ultracompanions.

Undirected and directed graphs with near polynomial growth

V.I. Trofimov (2003)

Discussiones Mathematicae Graph Theory

The growth function of a graph with respect to a vertex is near polynomial if there exists a polynomial bounding it above for infinitely many positive integers. In the paper vertex-symmetric undirected graphs and vertex-symmetric directed graphs with coinciding in- and out-degrees are described in the case their growth functions are near polynomial.

Uniform growth of groups acting on Cartan–Hadamard spaces

Gérard Besson, Gilles Courtois, Sylvestre Gallot (2011)

Journal of the European Mathematical Society

In this paper we investigate the growth of finitely generated groups. We recall the definition of the algebraic entropy of a group and show that if the group is acting as a discrete subgroup of the isometry group of a Cartan–Hadamard manifold with pinched negative curvature then a Tits alternative is true. More precisely the group is either virtually nilpotent or has a uniform growth bounded below by an explicit constant.

Unique a -closure for some -groups of rational valued functions

Anthony W. Hager, Chawne M. Kimber, Warren W. McGovern (2005)

Czechoslovak Mathematical Journal

Usually, an abelian -group, even an archimedean -group, has a relatively large infinity of distinct a -closures. Here, we find a reasonably large class with unique and perfectly describable a -closure, the class of archimedean -groups with weak unit which are “ -convex”. ( is the group of rationals.) Any C ( X , ) is -convex and its unique a -closure is the Alexandroff algebra of functions on X defined from the clopen sets; this is sometimes C ( X ) .

Units of the string link monoids

(2014)

Banach Center Publications

We show that the map obtained by viewing a geometric (i.e. representative) braid as a string link induces an isomorphism of the n-strand braid group onto the group of units of the n-strand string link monoid.

[unknown]

О.Г. Харлампович (1987)

Algebra i Logika

[unknown]

Nariya Kawazumi, Yusuke Kuno (0)

Annales de l’institut Fourier

[unknown]

Pierre-Emmanuel Caprace, David Hume (0)

Annales de l’institut Fourier

[unknown]

Marc Bourdon (0)

Annales de l’institut Fourier

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