Automorphism towers of polycyclic groups

Automorphism Towers and Automorphism Groups of Fields without Choice

Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construc...

Iteratively Changing the Heights of Automorphism Towers

We extend the results of Hamkins and Thomas concerning the malleability of automorphism tower heights of groups by forcing. We show that any reasonable sequence of ordinals can be realized as the automorphism tower heights of a certain group in consecutive forcing extensions or ground models, as desired. For example, it is possible to increase the height of the automorphism tower by passing to ...

Changing the Heights of Automorphism Towers

If G is a centreless group, then τ(G) denotes the height of the automorphism tower of G. We prove that it is consistent that for every cardinal λ and every ordinal α < λ, there exists a centreless group G such that (a) τ(G) = α; and (b) if β is any ordinal such that 1 ≤ β < λ, then there exists a notion of forcing P, which preserves cofinalities and cardinalities, such that τ(G) = β in the corr...

AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr

H"{o}lder in 1893 characterized all groups of order $pqr$ where  $p>q>r$ are prime numbers. In this paper,  by using new presentations of these groups, we compute their full automorphism group.