Related papers: Generalization of order separability for free grou…
Extending pioneering work by Weinberg, Conrad, McCleary, and others, we provide a systematic way of relating spaces of right orders on a partially ordered group, on the one hand, and spectral spaces of free lattice-ordered groups, on the…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
We investigate several boundedness properties of function spaces considered as uniform spaces.
We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…
We introduce the space of relative orders on a group and show that it is compact whenever the group is finitely generated. We use this to show that if $G$ is a finitely generated group acting by order preserving homeomorphism of on the…
In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.
This short note describes and proves a connectedness property which was introduced in Blocher et al. [2023] in the context of data depth functions for partial orders. The connectedness property gives a structural insight into union-free…
We study finite subgroups of outer automorphisms of free products. We give upper bounds for the orders of these finite subgroups as well as bounds for the orders of individual torsion outer automorphisms under some (necessary) conditions…
The abstract will be added in due course.
In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…
We give a classification of iwip outer automorphisms of the free group, by discussing the properties of their attracting and repelling trees.
We prove new separability results about free groups. Namely, if $H_1, \ldots , H_k$ are infinite index, finitely generated subgroups of a non-abelian free group $F$, then there exists a homomorphism onto some alternating group $f:F…
This is a biased survey for the Johnson homomorphisms of the automorphism groups of free groups. We just exposit some well known facts and recent developments for the Johnson homomorphisms and its related topics.
In this report we summarize this work, all finite simple groups $G$ can determined uniformly using their orders $|G|$ and the set $\pi_e(G)$ of their element orders.
A new generalization of the classical separate algebraicity theorem is suggested and proved.
This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals…
The object of observation in present paper is statistical independence of real sequences and its description as independence with re spect to certain class of densities.
In this paper we provide a sufficient condition for a subgroup of a free group not to have the almost congruence extension property (ACEP). We also show that any finitely generated subgroup of a free group satisfies some a generalization of…
The local to global property for an equation $\psi$ over a group G asks to show that $\psi$ is solvable in G if and only if it is solvable in every finite quotient of G. In this paper we focus that in order to prove this local to global…
In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.