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An automorphism a of a group G is called an artinian automorphism if for every strictly descending chain $H_1>H_2>\mathrm{\cdots }>H_n>\mathrm{\cdots }$ of subgroups of G there exists a positive integer $m$ such that ${(H_n)}^a=H_n$ for every $n\ge m$. In this paper we show that in many cases the group of all artinian automorphisms of $G$ coincides with the group of all power automorphisms of $G$.