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Let $\mathcal{G}^{(\lambda)}$ be a group scheme which deforms $\mathbb{G}_a$to $\mathbb{G}_m$. We explicitly describe the Cartier dual of the $l$-thFrobenius type kernel $N_l$ of the group scheme $\mathcal{E}^{(\lambda,\mu;D)}$which is an extension of $\mathcal{G}^{(\lambda)}$ by $\mathcal{G}^{(\mu)}$.Here we assume that the base ring $A$ is a $\mathbb{Z}_{(p)}$-algebracontaining some nilpotent elements. The obtained result generalizes a previousresult by N. Aki and M. Amano (Tsukuba J.Math. $\textbf{34}$ (2010)) whichassumes that $A$ is an $\mathbb{F}_p$-algebra.

On the Cartier duality of certain finite group schemes of order $p^n$, III