A Bers-like proof of the existence of train tracks for free group automorphisms
Using Lipschitz distance on Outer space we give another proof of the train track theorem.
A finiteness condition on automorphism groups
A note on central automorphisms of groups
A characterization of central automorphisms of groups is given. As an application, we obtain a new proof of the centrality of power automorphisms.
A note on -endomorphisms of two-generated metabelian groups
A note on locally graded groups
A note on the continuous extensions of injective morphisms between free groups to relatively fre profinite groups.
Let V be a pseudovariety of finite groups such that free groups are residually V, and let φ: F(A) → F(B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extension φ' of φ between the pro-V completions of F(A) and F(B) is also injective. In particular, if V is extension-closed, this is the case if and only if φ(F(A)) and its pro-V closure in F(B) have the same rank. We examine a number of situations where the injectivity of φ' can...
A note on the endomorphisms associated to semi-direct decompositions of a group
A remark about central automorphisms of groups
A theorem on groups
Addendum and corrigendum to «Automorfismi che fissano i centralizzanti di un gruppo»
Almost fixed-point-free automorphisms of prime order
Let ϕ be an automorphism of prime order p of the group G with C G(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived length are...
Amenability of linear-activity automaton groups
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.
Anwendungen der Nielsenschen Kürzungsmethode in Gruppen mit einer definierenden Relation.
Automorfismi che fissano i centralizzanti di un gruppo
Automorphism groups of free metabelian nilpotent groups.
Automorphismen und Erzeugende für Gruppen mit einer definierenden Relation.
Automorphismengruppen von Gruppen mit endlichen Bahnen gleichmäßig beschränkter Mächtigkeit.
Automorphisms fixing every Normal Subgroup of a Nilpotent-by-abelian Group
Automorphisms of free groups and their fixed points.
Automorphisms of linear semigroups over division rings.