arXiv subjects

Noureddine Snanou

Publications and source records attributed to Noureddine Snanou.

3 recordsLinked to original sources

arXiv2024

On the isomorphism problem for central extensions I

Let $G_{2}$ be a group which acts trivially on an abelian group $G_{1}$. As is well known, each perturbed direct product of $G_{1}$ and $G_{2}$ under a 2-cocycle $\varepsilon\in Z^{2}(G_{2},G_{1})$ determines a central extension of $G_{1}$ by $G_{2}$. The purpose of this paper is to study perturbed direct products of groups and to decide in some cases how the isomorphism of these groups can be decided. Furthermore, we show that the study of the isomorphism of perturbed direct products of an abelian torsion group and a finite group is reduced to the study of the isomorphism of $p$-subgroups. We characterize such isomorphisms in various situations with some assumptions on the quotient group.

math.GR↗

arXiv2024

On the isomorphism problem for central extensions II

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.

math.GR↗

arXiv2022

On p-groups of maximal class

Recall that a $p$-group of order $p^ {n} >p^ {3} $ is of maximal class, if its nilpotency class is $n-1$. In this paper, we study the $p$-groups of maximal class. Furthermore, we introduce a subgroup of a $p$-group of maximal class called the fundamental subgroup. This group plays a fundamental role in the development of the general theory of $p$-groups of maximal class. As an application, we study some special class of finite $p$-groups of maximal class and exponent $p$.

math.GR↗