Related papers: Groups of Intermediate Growth: an Introduction for…
This paper explores middle-grade students' conceptions of median. Describes, where and why they struggle and provides learning trajectory to improve their understanding.
In the following text we introduce the concept of pseudo-codecomposition of a transformation group, also we show the collection of all transformation groups pseudo-codecomposable to distal ones is a proper intermediate class of the class of…
These notes give a short introduction to finite Coxeter groups, their classification, and some parts of their representation theory, with a focus on the infinite families. They are based on lectures delivered by the author at the…
The abstract will be added in due course.
The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in other…
We discuss the notion of growth for discrete quantum groups, with a number of general considerations, and with some explicit computations. Of particular interest is the quantum analogue of Gromov's estimate regarding polynomial growth: we…
This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.
We consider the growth of an infinite family of finite groups. We are motivated by the remarkable contribution of Bass, Wolf, Milnor, Gromov, Grigorchuk on the word growth and structure of infinite groups, and the results of Black on the…
Recently, group recommendations have attracted considerable attention. Rather than recommending items to individual users, group recommenders recommend items to groups of users. In this position paper, we introduce the problem of forming an…
We partly generalize the estimate for the rank of intersection of subgroups in free products of groups, proved earlier by S.V.Ivanov and W.Dicks, to the case of free amalgamated products of groups with normal finite amalgamated subgroup. We…
In this work, we estimate the genus of the intermediate modular curves between $X_1(N)$ and $X_0(N),$ and determine all the trigonal ones.
We describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult…
Consider a relatively hyperbolic group G. We prove that if G is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of G, a solution of its…
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural transformations between Lie groupoid morphisms.
Grigorchuk's Overgroup $\tilde{\mathcal{G}}$, is a branch group of intermediate growth. It contains the first Grigorchuk's torsion group $\mathcal{G}$ of intermediate growth constructed in 1980, but also has elements of infinite order. It's…
We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups. A detailed study of the uniform exponential growth rate of closed 3-manifold groups is also presented.
We give a sufficient condition for a sequence of normal subgroups of a free group to have the property that both, their growths tend to the upper bound and their cogrowths tend to the lower bound. The condition is represented by planarity…
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.