Article in press
Authors:
Noureddine Snanou
Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
Title:
On the isomorphism problem for knit products
PDFSource:
Discussiones Mathematicae - General Algebra and Applications
Received: 2023-12-21 , Revised: 2024-05-19 , Accepted: 2024-05-20 , Available online: 2024-08-22 , https://doi.org/10.7151/dmgaa.1460
Abstract:
In this paper, we classify up to isomorphism the groups that can be represented as knit products of two groups. More precisely, some necessary and sufficient conditions for two knit products to be isomorphic are given. We mainly deal with isomorphisms leaving one of the two factors or even both invariant. In particular, we decide under some conditions how the knit products arise as split extensions. Furthermore, the decomposition of unfaithful knit products is investigated.
Primary keywords:
Knit product, lower isomorphic, upper isomorphic
Secondary keywords:
diagonally isomorphic, factorization problem
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