Configuration of nilpotent groups and isomorphism

A. Abdollahi; A. Rejali; A. Yousofzadeh

paper

Configuration of nilpotent groups and isomorphism

arXiv:0811.2291

Abstract

The concept of configuration was first introduced by Rosenblatt and Willis to give 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 $G_{1}$ with abelian quotient, then there is a normal subgroup $H_{2}$ of $G_{2}$ such that $\frac{G _{1}}{H _{1}} ≅ \frac{G _{2}}{H _{2}} .$ Also configuration of FC-groups and isomorphism is studied.

to appear in Journal of Algebra and its Applications