TY - JOUR
AU - Tavakoli, Ali
AU - Rejali, Ali
AU - Yousofzadeh, Akram
AU - Abdollahi, Alireza
PY - 2014/12/01
Y2 - 2023/12/05
TI - A Note About Configuration Of A Group
JF - MATEMATIKA
JA - MATEMATIKA
VL - 30
IS - 0
SE - Mathematics
DO - 10.11113/matematika.v30.n.703
UR - https://matematika.utm.my/index.php/matematika/article/view/703
SP - 117-121
AB - In 2001, Rosenblatt and Willis defined the concept of configuration of a group to give a condition for amenability of groups. In this paper, we study the relation between 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 = G2/G'2 and if G'1 and G'2 are finite, then G'1 = G'2 2. Also, we prove that if two free finitely generated Burnside groups of finite exponent have the same configuration set, then they must be isomorphic. Keywords: Configuration; Amenability; Commutator Subgroup, Burnside Group 2010 Mathematics Subject Classification: 20F24, 43A07.
ER -