  In the present work we investigate a subgroup $I_n$ of the McCool group
$M_n$. We show that $I_n$ has solvable conjugacy problem. Next, we investigate
its Lie Algebra gr($I_n$) and we find a presentation for it. Finally we show
that gr($I_n$) is naturally embedded into the Andreadakis-Johnson Lie Algebra
of the IA automorphisms of the free group $F_n$.
