Configuration of nilpotent groups and isomorphism

2008/11/14 by Aliréza Abdollahi, A. Abdollahi, Ali Rejali +6
Engineering · Mathematics · #20F99 #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR #msc:20F99

paper · pdf · doi:10.48550/arxiv.0811.2291

to appear in Journal of Algebra and its Applications

arxiv created 2008/11/14 · openalex publication_date 2008/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The concept of configuration was first introduced by Rosenblatt and Willis to give a condition for amenability of groups. We show that if G₁ and G₂ have the same configuration sets and H₁ is a normal subgroup of G₁ with abelian quotient, then there is a normal subgroup H₂ of G₂ such that (G₁)/(H₁)≅(G₂)/(H₂). Also configuration of FC-groups and isomorphism is studied.

Related

• Configuration Equivalence is not Equivalent to Isomorphism
• Two-sided configuration equivalence and isomorphism
• Solubility of groups can be characterized by configuration
• Groups isomorphic to all their non-trivial normal subgroups
• Automorphisms fixing every normal subgroup of a nilpotent-by-abelian group