Let $G$ be a group and $Aut(G)$ be the group of automorphisms of$G$. For any naturalnumber $m$, the $m^{th}$-autocommutator subgroup of $G$ is definedas: $$K_{m} (G)=\langle[g,\alpha_{1},\ldots,\alpha_{m}] |g\in G&l
أکثر
Let $G$ be a group and $Aut(G)$ be the group of automorphisms of$G$. For any naturalnumber $m$, the $m^{th}$-autocommutator subgroup of $G$ is definedas: $$K_{m} (G)=\langle[g,\alpha_{1},\ldots,\alpha_{m}] |g\in G,\alpha_{1},ldots,\alpha_{m}\in Aut(G)\rangle.$$In this paper, we obtain the $m^{th}$-autocommutator subgroup ofall finite abelian groups.
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