Groups of automorphisms of the free group I. Transvections

[摘要] In this study we define a new family of free automorphisms tailed transvections 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 fee differential calculus. The groups generated by these automorphisms form the family of transvection 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. (C) 2000 Academic Press.

[发布日期] 1999-12-15