Iteratively Changing the Heights of Automorphism Towers

Changing the heights of automorphism towers by forcing with Souslin trees over L

We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid non-isomorphic Souslin trees whose isomorphism relation can be precisely controlled by forcing.

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 Towers and Automorphism Groups of Fields without Choice

Asymptotic aspects of Schreier graphs and Hanoi Towers groups

We present relations between growth, growth of diameters and the rate of vanishing of the spectral gap in Schreier graphs of automaton groups. In particular, we introduce a series of examples, called Hanoi Towers groups since they model the well known Hanoi Towers Problem, that illustrate some of the possible types of behavior. 1 Actions on rooted trees, automaton groups, and Hanoi Towers group...

The Automorphism Tower

It is well-known that the automorphism towers of infinite centre-less groups of cardinality κ terminate in less than (2 κ) + steps. But an easy counting argument shows that (2 κ) + is not the best possible bound. However, in this paper, we will show that it is impossible to find an explicit better bound using ZF C.