Let Fn = 〈x1, …, xn〉
denote the free group with generators {x1, …,
xn}. Nielsen and Magnus described generators for the kernel of
the canonical epimorphism from the automorphism group of Fn
to the general linear group over the integers. In particular among them
are the automorphisms χk,i which conjugate the generator
xk by the generator xi leaving the xj
fixed for j not k. A computation of the cohomology ring as well as
the Lie algebra obtained from the descending central series of the
group generated by χk,i for i < k is given here. Partial
results are obtained for the group generated by all χk,i.
Département des Sciences
Mathématiques
Université Montpellier II
Place Eugéne Bataillon
34095 Montpellier cedex 5
France
and
Sobolev Institute of Mathematics
Novosibirsk, 630090
Russia