Automorphism groups of diagonal $\mathbf Z_p$-forms of the Lie algebra $sl_2(\mathbf Q_p)$, $p>2$

A. V. Yushchenko's paper [Sib. Mat. Zh., 43, No. 5, 1197–1207] implies that two nondiagonal forms like $S(n,d)+\mathbf Z_pA$ and $S(n,d)+\mathbf Z_pA'$ are isomorphic if the elements of $A$ and $A'$ are conjugated via the group $\mathrm{Aut}_{\mathbf Z_p}S(n,d)$. In the present paper, we settle just this question on conjugation. In other words, we describe the group $\mathrm{Aut}_{\mathbf Z_p}S(n,d)$ and clarify under which conditions two elements of $S(n,d)$ are conjugate under the action of this group on $S(n,d)$, $p>2$.