Determination of M-Power Soft Subgroup Structures

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

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: ‎$$k_{m}(g)=langle[g,alpha_{1},ldots,alpha_{m}] |gin g‎,‎alpha_{1},ldots,alpha_{m}in aut(g)rangle.$$‎‎in this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎‎all finite abelian groups‎.

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ژورنال

عنوان ژورنال: International Journal for Research in Applied Science and Engineering Technology

سال: 2019

ISSN: 2321-9653

DOI: 10.22214/ijraset.2019.10092