On Non-split Abelian Extensions

Snanou, Noureddine; Charkani, Mohammed Elhassani

doi:10.1007/s41980-020-00410-9

Cited by 2 publications

(7 citation statements)

References 12 publications

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“…So, we have φ 21 • ε 1 = 1 and then φ 22 ∈ End(G 2 ). Furthermore, by using the 2-cocycle condition, the equation (10) gives us…”

Section: Let Prmentioning

confidence: 99%

“…As mentioned in the introduction, our choice to focus on the isomorphism problem for extensions with abelian kernel group is partially motivated by the Jordan-Hölder Theorem. Our other works of particular relevance are [8][9][10][11]. We study in [11] the isomorphism problem for split extensions, and as an application, we determine how isomorphism of split extensions and conjugacy of the images of the corresponding actions are related.…”

Section: Conclusion and Future Problemsmentioning

confidence: 99%

“…However, this answer will not enable us to construct all possible non-isomorphic central extensions of G 1 by G 2 (the isomorphism problem). In fact, it is very hard to solve the isomorphism problem, but it has been discussed for some special cases in [8][9][10]. In fact, those results do not concern general isomorphisms, but only those of certain type, namely leaving the kernel group or both the two factors invariant, inducing the identity or a commuting automorphism on the quotient group.…”

Section: Introductionmentioning

confidence: 99%

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On the Isomorphism Problem for Central Extensions II

Snanou

2024

Eur. J. Pure Appl. Math.

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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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“…So, we have φ 21 • ε 1 = 1 and then φ 22 ∈ End(G 2 ). Furthermore, by using the 2-cocycle condition, the equation (10) gives us…”

Section: Let Prmentioning

confidence: 99%

Section: Conclusion and Future Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Isomorphism Problem for Central Extensions II

Snanou

2024

Eur. J. Pure Appl. Math.

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“…Very recently, we study in [12] the isomorphism problem for split extensions. In [11,13], we characterize the isomorphism problem for non-split abelian extensions. In fact, most of the results of those studies do not concern general isomorphisms, but only those of certain type, namely leaving one of the two factors or even both invariant.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the isomorphism problem for split extensions

Snanou¹,

Charkani²

2022

J. Algebra Appl.

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In this paper, we study an important well-known structure operation, namely, the semidirect product (or split extensions) which is a very useful tool to structure certain kinds of groups. More precisely, we study the isomorphism problem for semidirect products and then we determine how isomorphism of semidirect products and conjugacy of the images of the corresponding actions are related. As an application, for two positive integers [Formula: see text] and [Formula: see text], we compute the number of upper isomorphism classes of split extensions of an elementary abelian [Formula: see text]-group of order [Formula: see text] by an elementary abelian [Formula: see text]-group of order [Formula: see text]. Furthermore, we deal with split extensions where the kernel is a non-abelian [Formula: see text]-group of nilpotency class two and the quotient is an elementary abelian [Formula: see text]-group.

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On Non-split Abelian Extensions

Cited by 2 publications

References 12 publications

On the Isomorphism Problem for Central Extensions II

On the Isomorphism Problem for Central Extensions II

On the isomorphism problem for split extensions

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