Automorphisms of free groups. I — erratum
نویسندگان
چکیده
I report an error in Theorem A of Automorphisms of free groups. I , New York J. Math. 19 (2013), 395–421, where it was claimed that two filtrations of the group of IA automorphisms of a free group coincide up to torsion. In fact, using a recent result by Day and Putman, I show that, for a free group of rank 3, the opposite conclusion holds, namely that the two series differ rationally.
منابع مشابه
Some Remarks on Commuting Fixed Point Free Automorphisms of Groups
In this article we will find necessary and sufficient conditions for a fixed point free automorphism (fpf automorphism) of a group to be a commuting automorphism. For a given prime we find the smallest order of a non abelian p-group admitting a commuting f...
متن کاملSome properties of marginal automorphisms of groups
AbstractLet W be a non-empty subset of a free group. The automorphism of a group G is said to be a marginal automorphism, if for all x in G,x^−1alpha(x) in W^*(G), where W^*(G) is the marginal subgroup of G.In this paper, we give necessary and sufficient condition for a purelynon-abelian p-group G, such that the set of all marginal automorphismsof G forms an elementary abelian p-group.
متن کاملGeodesic Currents and Length Compactness for Automorphisms of Free Groups
We prove a compactness theorem for automorphisms of free groups. Namely, we show that the set of automorphisms keeping bounded the length of the uniform current is compact (up to conjugation.) This implies that the spectrum of the length of the images of the uniform current is discrete, answering to a conjecture of I. Kapovich.
متن کاملOn Automorphism Groups of Free Products of Finite Groups, I: Proper Actions
If G is a free product of finite groups, let ΣAut1(G) denote all (necessarily symmetric) automorphisms of G that do not permute factors in the free product. We show that a McCullough-Miller [D. McCullough and A. Miller, Symmetric Automorphisms of Free Products, Mem. Amer. Math. Soc. 122 (1996), no. 582] and Gutiérrez-Krstić [M. Gutiérrez and S. Krstić, Normal forms for the group of basis-conjug...
متن کاملExtending Partial Automorphisms and the Proonite Topology on Free Groups
A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C 1 and C 2 are structures in C, C 1 nite, C 1 C 2 , and p 1 , p 2 , : : :, p n are partial automorphisms of C 1 extending to automorphisms of C 2 , then there exist a nite structure C 3 in C and automorphisms 1 , 2 , : : :, n of C 3 extending the p i. We will prove that some classes of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016