Sur le groupe d'automorphismes du groupe libre I. Transvections

✍ Scribed by Daniel Piollet

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 375 KB
• Volume: 222
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8036

✦ Synopsis

In this study we define a new family of free automorphisms called trans¨ections which generalise the Whitehead automorphisms. This leads to a new presentation of the group of free automorphisms and to a partial generalisation of McCool's well known result on the presentation of certain of its subgroups. We study the ''linear'' characteristics of transvections with the use of Fox free differential calculus. The groups generated by these automorphisms form the family of trans¨ection groups that one could name the pre-classical groups. We give some simple examples of these groups, which we shall study further throughout the following papers.