The Permutizer Condition in Infinite Soluble Groups

groups of infinite rank with a normalizer condition on subgroups

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

A relation between infinite subsets and exterior center in groups

Let G be a group. Neumann to answer a question of Paul Erdos proved that every infinite subset of G has two different comuting elements  if and only if G is center-by-finite. In this paper, we deal with Erdoschr('39')s question in different aspect and we show that every infinite subset X of G has two different elements x and y such that x^y=1  if and only if the exterior  center of G ihas finit...

Topics in Infinite Groups

Preface These are lecture notes for a course taught in Cambridge during Lent 2014 by Jack Button, on a topics in infinite group theory. There are likely to be errors, which are solely the fault of the scribe. If you discover any, please contact me [email protected].

Infinite Groups

Most interesting groups arise as a group of transformations. For example the set of “rigid motions” of 2-dimensional space R forms a group denoted Isom(R). There are three kinds of transformations: reflection about a line, rotation about a point, and translation in a direction. These form a group under composition (i.e., do one transformation and then do the other). For example, the composition...

Expansion in Soluble Groups