# Configuration of nilpotent groups and isomorphism - Mathematics > Group Theory

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Abstract: The concept of configuration was first introduced by Rosenblatt and Willis togive a condition for amenability of groups. We show that if $G 1$ and $G 2$have the same configuration sets and $H 1$ is a normal subgroup of $G 1$ withabelian quotient, then there is a normal subgroup $H 2$ of $G 2$ such that$\frac{G 1}{H 1}\cong\frac{G 2}{H 2}.$ Also configuration of FC-groups andisomorphism is studied.

Autor: A. Abdollahi, A. Rejali, A. Yousofzadeh

Fuente: https://arxiv.org/