On $m^{th}$-autocommutator subgroup of finite abelian groups
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Abstract:
Let $G$ be a group and $Aut(G)$ be the group of automorphisms of $G$. For any natural number $m$, the $m^{th}$-autocommutator subgroup of $G$ is defined as: $$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G,alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$ In this paper, we obtain the $m^{th}$-autocommutator subgroup of all finite abelian groups.
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Journal title
volume 05 issue 02
pages 135- 144
publication date 2016-09-01
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