|
Title:
|
Bounding the gap between a free group (outer) automorphism and its inverse
|
|
Author:
|
Ladra, Manuel; Silva, Pedro V.; Ventura Capell, Enric
|
|
Other authors:
|
Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta |
|
Abstract:
|
The final publication is available at Springer via http://dx.doi.org/10.1007/s13348-015-0133-3. |
|
Abstract:
|
For any finitely generated group GG , two complexity functions aGaG and ßGßG are defined to measure the maximal possible gap between the norm of an automorphism (respectively, outer automorphism) of GG and the norm of its inverse. Restricting attention to free groups FrFr , the exact asymptotic behaviour of a2a2 and ß2ß2 is computed. For rank r¿3r¿3 , polynomial lower bounds are provided for arar and ßrßr , and the existence of a polynomial upper bound is proved for ßrßr . |
|
Abstract:
|
Peer Reviewed |
|
Subject(s):
|
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
-Free groups
-Group theory
-Automorphisms
-Automorphism
-Inverse automorphism
-Norm of an automorphism
-Free group
-Grups, Teoria de
-Automorfismes
-Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups
-Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups |
|
Rights:
|
|
|
Document type:
|
Article - Submitted version
Article |
|
Share:
|
|
