On The Group Of Pointwise Inner Automorphisms

Let $L_{m,c}$ stand for the free metabelian nilpotent Lie algebra of class $c$ rank $m$ over a field $K$ characteristic zero.
 Automorphisms form $\varphi(x_i)=e^{adu_i}(x_i)$ are called pointwise inner, where $e^{adu_i}$, is inner automorphism
 induced by element $u_i\in L_{m,c}$ each $i=1,\ldots,m$. In present study, we investigate group structure of
 $\text{\rm PInn}(L_{m,c})$ automorphisms low nilpotency classes.