Construction of po-groups with quasi-divisors theory

Proceedings of the American Mathematical Society, 1967

Journal of Algebra, 2000

Cornell University - arXiv, 2022

Fontaine-Mazur Conjecture is one of the core statements in modern arithmetic geometry. Several formulations were given since its original statement in 1993, and various angles have been adopted by numerous authors to try to tackle it. Among those, a range of tools that is not so well-known among young arithmetic geometers, goes back to Boston's seminal paper in 1992, and relies on purely group-theoretic methods (rather than representation-theoretic ones) to prove some special cases of this conjecture. Such methods have been later successfully carried on by Maire and his co-authors, and brings different informations on the objects involved in the conjecture. This survey article aims to review what is known in this direction and to present some interesting related questions the authors (aim to) work on.

arXiv: Group Theory, 2008

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties and invariants of groups invariant under quasiisometry, rigidity, hyperbolic spaces and CAT(k)-spaces, the boundary of a hyperbolic space, hyperbolic groups, CAT(0)-groups, classifying spaces for proper actions, measurable group theory, some open problems.

Czechoslovak Mathematical Journal, 1977

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Revista Matematica Iberoamericana, 2002

In this paper we will prove that if $G$ is a finite group, $X$ a subnormal subgroup of $ X F^*(G)$ such that $X F^*(G)$ is quasinilpotent and $Y$ is a quasinilpotent subgroup of $N_G(X)$, then $Y F^*(N_G(X})$ is quasinilpotent if and only if $Y F^*(G)$ is quasinilpotent. Also we will obtain that $F^*{G}$ controls its own fusion in $G$

Colloquium Mathematicum, 1978

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

2019

This thesis aims to serve as an introduction to the theory of quasitilings for amenable groups. In order to showcase the power of this theory, we focus on the study of the Sofic L\"uck Approximation Conjecture, which can be proven for amenable groups by making use of quasitilings. The first four chapters of the thesis are an exposition of the aforementioned topics, collected from the literature. After that, in the fifth and final chapter we present some new results related to the Sofic L\"uck Approximation Conjecture for amenable groups over discrete valuation rings and number fields.