On the isomorphism problem for central extensions II

2024/02/12 by Noureddine Snanou, Snanou, Noureddine
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Rings, Modules, and Algebras #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2402.07679

openalex publication_date 2024/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the isomorphism problem for central extensions. More precisely, in some new situations, we provide necessary and sufficient conditions for two central extensions to be isomorphic. We investigate the case when the quotient group is simple or purely non-abelian. Furthermore, we characterize isomorphisms leaving the quotient group invariant. Finally, we deal with isomorphisms of central extensions where the kernel group and the quotient group are isomorphic.

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