arXiv subjects

Abdallah Shihadeh

Publications and source records attributed to Abdallah Shihadeh.

3 recordsLinked to original sources

arXiv2024

The Number of Subgroups and Cyclic Subgroups of Finite Group and Its Application by GAP Program

In this paper, we present a novel approach for calculating the set of subgroups of a finite group, focusing on cyclic subgroups, and using it to establish the quantity of all subgroups in the direct product of two groups. Specifically, we consider the Dicyclic group of order $4n$ and the Cyclic group of order $p$. Let $τ(n)$ denote the total number of divisors of $n$, and $σ(n)$ denote the summation of all divisors of $n$. Using these functions, we derive a formula for the number of subgroups in the group $T_{4n} \times C_p$. We then use the computer program GAP to find all $T_{4n} \times C_p$ with exactly $|T_{4n} \times C_p| - t$ cyclic subgroups for $t \geq 1$.

math.GR↗

arXiv2023

Graded prime ideals over graded Lie algebras

In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to those about graded prime ideals over a commutative or non-commutative ring.In addition, the ideas of graded semiprime Lie ideals and graded total prime Lie ideals will be introduced.

math.RA↗

arXiv2019

Graded torsion-free ${\mathfrak{sl}_2(\mathbb{C})}$-modules of rank 2

In this paper we explore the possibility of endowing simple infinite-dimensional ${\mathfrak{sl}_2(\mathbb{C})}$-modules by the structure of the graded module. The gradings on finite-dimensional simple module over simple Lie algebras has been studied in [arXiv:1308.6089] and [arXiv:1601.03008].

math.RA↗