Research ArticleNo Access

On non-split abelian extensions II

Noureddine Snanou

Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco

E-mail Address: noureddine.snanou@usmba.ac.ma

https://doi.org/10.1142/S1793557121501643Cited by:1 (Source: Crossref)

Abstract

Let $G_{2}$ be a group acting on an abelian group $G_{1}$ via a homomorphism $α \in Hom (G_{2}; Aut (G_{1}))$ and let a 2-cocycle $𝜀 \in Z^{2} (G_{2}, G_{1}, α)$ . By Schreier’s theorem, the pair $(α, 𝜀)$ determines a group $G_{(α, 𝜀)}$ which can arise as a non-split extension of $G_{1}$ by $G_{2}$ , denoted by $G_{1} \underset{(α, 𝜀)}{\times} G_{2}$ and called the perturbed semidirect product of $G_{1}$ by $G_{2}$ under $(α, 𝜀)$ . In this paper, we classify the perturbed semidirect products and give some of their properties. Furthermore, we find necessary and sufficient conditions for two perturbed semidirect products to be isomorphic.

Communicated by V. A. Artamanov

Keywords:

AMSC: 20J05, 20J06

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