Jordan’s theorem for solvable groups

Freiman's theorem for solvable groups

Freiman’s theorem asserts, roughly speaking, if that a finite set in a torsion-free abelian group has small doubling, then it can be efficiently contained in (or controlled by) a generalised arithmetic progression. This was generalised by Green and Ruzsa to arbitrary abelian groups, where the controlling object is now a coset progression. We extend these results further to solvable groups of bo...

A Rigidity Theorem for the Solvable Baumslag-solitar Groups

refined solvable presentations for polycyclic groups

‎we describe a new type of presentation that‎, ‎when consistent‎, ‎describes a polycyclic group‎. ‎this presentation is obtained by‎ ‎refining a series of normal subgroups with‎ ‎abelian sections‎. ‎these presentations can be described effectively in‎ ‎computer-algebra-systems like {scshape gap} or ‎{scshape magma}‎. ‎we study these ‎presentations and‎, ‎in particular‎, ‎we obtain consistency c...

Arithmetic of Fields Safarevi C's Theorem on Solvable Groups as Galois Groups I

The organizers of the meeting were Wulf-Dieter Geyer (Erlangen) and Moshe Jarden (Tel Aviv). The 26 talks that were given during the conference fall (roughly) into several categories: 1. Fundamental groups and covers in characteristic p In the rst of two talks on the famous theorem of Safarevi c \Every nite solvable group occurs as a Galois group over a global eld" this result was composed with...

Characterization of Solvable Groups and Solvable radical

We give a survey of new characterizations of finite solvable groups and the solvable radical of an arbitrary finite group which were obtained over the past decade. We also discuss generalizations of these results to some classes of infinite groups and their analogues for Lie algebras. Some open problems are discussed as well.