Author/Authors :
Tavakoli, Ali university of isfahan - Department of Mathematics, اصفهان, ايران , Rejali, Ali university of isfahan - Department of Mathematics, اصفهان, ايران , Yousofzadeh, Akram Islamic Azad University, Mobarakeh Branch - Department of Mathematics, ايران , Abdollahi, Alireza university of isfahan - Department of Mathematics, اصفهان, ايران
Abstract :
In 2001, Rosenblatt and Willis defined the concept of configuration of agroup to give a condition for amenability of groups. In this paper, we study the relationbetween configuration and commutator subgroup G΄ of G and prove that if G1 and G2 are two finitely generated groups with the same configuration set, then G1/G΄1(approximately equal to) G2/G΄2and ifG΄1 and G΄2 are finite, then G΄1(approximately equal to)G΄2. Also, we prove that if two free finitely generatedBurnside groups of finite exponent have the same configuration set, then they must beisomorphic.
Keywords :
Configuration , Amenability , Commutator Subgroup , Burnside Group
