On $m^{th}$-autocommutator subgroup of finite abelian groups

Journal of Linear and Topological Algebra

مقاله 7، دوره 05، شماره 02، مرداد 2016، صفحه 135-144   

نوع مقاله: Research Paper

نویسندگان

A. Gholamian^{* 1، 2}؛ M. M. Nasrabadi³

¹Department of Mathematics, Birjand Education, Birjand, Iran

²Farhangian University, Shahid Bahonar Campus, Birjand, Iran

³Department of Mathematics, University of Birjand, Birjand, Iran

چکیده

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: ‎$$K_{m} (G)=\langle[g,\alpha_{1},\ldots,\alpha_{m}] |g\in G‎,\‎alpha_{1},ldots,\alpha_{m}\in Aut(G)\rangle.$$‎ ‎In this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎ ‎all finite abelian groups‎.

کلیدواژه‌ها

‎Automorphism‎؛ ‎Lower autocentral series‎؛ ‎Finite Abelian group

مراجع

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