Abstract

On Permutable Subgroups of n-ary Groups

Highlights

  • We remind that, the system G = < X, ( )> with one n-ary operation ( ) is called n-ary group[1,2], if it is associative and every one of the equations.(a1 a2 .... ai-1 x ai+1 ...... an) = a is solvable in X, where a1, ... an, a ∈ X, i = 1, 2, ..., n

  • It is proved that every permutable subgroup of a finite n-ary group is subnormal

  • Proof: Let D any subgroup of n-ary group G, by Definition 2: Let G be n-ary group and let x ∈ G, the sequence of elements x of G is called an inverse of x if xx is an identity

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Summary

Introduction

Abstract: It is proved that every permutable subgroup of a finite n-ary group is subnormal. Be n-ary group and let H is a subgroup of G, H is called permutable n-ary group if HT=TH for all subgroups T of G. Subgroup H of n-ary group G is called permutable if for any subgroup T from G we have

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