Configuration of nilpotent groups and isomorphism

Details Configuration of nilpotent groups and isomorphism Configuration of nilpotent groups and isomorphism

2008-11-14

arxiv.org/abs/0811.2291v1

Mathematics

Group Theory

to appear in Journal of Algebra and its Applications

Scientific paper

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 $\frac{G_1}{H_1}\cong\frac{G_2}{H_2}.$ Also configuration of FC-groups and isomorphism is studied.

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