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Papers by rola hijazi

Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle R... more Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Abstract. The aim of the present work is centered around the tautness property for the two K-type... more Abstract. The aim of the present work is centered around the tautness property for the two K-types of Alexander-Spanier cohomology given by the authors. A version of the con-tinuity property is proved, and some applications are given. 2000 Mathematics Subject Classification. Primary 55N05, 55N20, 55N35. 1. Introduction. It

Discrete Mathematics & Theoretical Computer Science, 2015

Graph Theory International audience Ruskey and Savage conjectured that in the d-dimensional hyper... more Graph Theory International audience Ruskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle. Fink verified this for every perfect matching M, remarkably even if M contains external edges. We prove that this property also holds for sparse spanning regular subgraphs of the cubes: for every d ≥7 and every k, where 7 ≤k ≤d, the d-dimensional hypercube contains a k-regular spanning subgraph such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle. We do not know if this result can be extended to k=4,5,6. It cannot be extended to k=3. Indeed, there are only three 3-regular graphs such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle, namely the complete graph on 4 vertices, the complete bipartite 3-regular graph on 6 vertices and the 3-cube on 8 vertices. Also, we do not know if there are graphs of girth at least 5 with this matc...

Let Z be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividin... more Let Z be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, Z contains exactly one and only one Sylow p-subgroup of G. A subgroup H of G is said to be Z-permutable of G if H permutes with every member of Z. A subgroup H of G is said to be a weakly Z-permutable subgroup of G if there exists a subnormal subgroup K of G such that G = HK and H ∩K ≤ HZ, where HZ is the subgroup of H generated by all those subgroups of H which are Zpermutable subgroups of G. We investigate the structure of the finite group G under the assumption that every cyclic subgroup of prime order p or of order 4 (if p = 2) is a weakly Z-permutable subgroup of G. Our results extend and generalize several results in the literature.

Journal of Advances in Mathematics, 2015

Let G be a nite group. A subgroup H of G is said to be c-normal in G if there exists a normal su... more Let G be a nite group. A subgroup H of G is said to be c-normal in G if there exists a normal subgroup K of G such that G = HK and H \ K HG, where HG is the largest normal subgroup of G contained in H. In this note we prove that if every Sylow subgroup P of G has a subgroup D such that 1 <jDj<jPj and all subgroups H of P with jHj=jDj are c-normal (S-permutable) in G, then G is solvable. This results improve and extend classical and recent results in the literature.

Cryptography and Communications, 2021

The original version of this article unfortunately missed to include another Acknowledgments belo... more The original version of this article unfortunately missed to include another Acknowledgments below. "The authors acknowledge the financial support provided by the NSTIP strategic technologies program in the Kingdom of Saudi Arabia-Project No (12-MAT3055-03), and extend the thanks to the Science and Technology Unit, King Abdulaziz University for their technical support." The original paper was updated.

Quantum Information Processing, 2021

European Journal of Pure and Applied Mathematics, 2021

Let G be a finite group. A subgroup H of G is called SS-quasinormal in G if there is a supplement... more Let G be a finite group. A subgroup H of G is called SS-quasinormal in G if there is a supplement B of H to G such that H permutes with every Sylow subgroup of B. A subgroup H of G is called CSS-subgroup in G if there exists a normal subgroup K of G such that G = HK and H âˆ©K is SS-quasinormal in G. In this paper, we investigate the influence of minimal CSS-subgroups of G on its structure. Our results improve and generalize several recent results in the literature.

European Journal of Pure and Applied Mathematics, 2019

Let G be a finite group. A subgroup H of G is said to be S-permutable in G if itpermutes with all... more Let G be a finite group. A subgroup H of G is said to be S-permutable in G if itpermutes with all Sylow subgroups of G. In this note we prove that if P, the Sylowp-subgroup of G (p > 2), has a subgroup D such that 1

Communications in Algebra, 2017

Let Z be a complete set of Sylow subgroups of a nite group G, that is, a set composed of a Sylow ... more Let Z be a complete set of Sylow subgroups of a nite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called Z-S-semipermutable if H permutes with every Sylow p-subgroup of G in Z for all p / ∈ π(H); H is said to be Z-S-seminormal if it is normalized by every Sylow p-subgroup of G in Z for all p / ∈ π(H). The main aim of this paper is to characterize the Z-MS-groups, or groups G in which the maximal subgroups of every Sylow subgroup in Z are Z-S-semipermutable in G and the Z-MSN-groups, or groups in which the maximal subgroups of every Sylow subgroup in Z are Z-S-seminormal in G.

Journal of Systems Science and Complexity, 2017

This paper constructs a cyclic Z4-code with a parity-check matrix similar to that of Goethals cod... more This paper constructs a cyclic Z4-code with a parity-check matrix similar to that of Goethals code but in length 2 m + 1, for all m ≥ 4. This code is a subcode of the lifted Zetterberg code for m even. Its minimum Lee weight is shown to be at least 10, in general, and exactly 12 in lengths 33, 65. The authors give an algebraic decoding algorithm which corrects five errors in these lengths for m = 5, 6 and four errors for m > 6.

Mediterranean Journal of Mathematics, 2017

All groups presented in this article are finite. Using several permutability embedding properties... more All groups presented in this article are finite. Using several permutability embedding properties, a number of new characterisations of soluble PST-groups are studied.

$Research paper thumbnail of The influence of weakly <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="fraktur">Z</mi></mrow><annotation encoding="application/x-tex">\mathfrak{Z}</annotation></semantics></math>Z-permutable subgroups on the structure of finite groups$

Publicationes Mathematicae Debrecen, 2016

A subgroup of a finite group G is said to be S-quasinormal in G if it permutes with every Sylow s... more A subgroup of a finite group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a finite group G is said to be s-semipermutable in G if it permutes with every Sylow p-subgroup of G, where p and the order of H are relatively prime. A subgroup H of a finite group G is said to be S-quasinormally embedded in G if every Sylow subgroup of H is a Sylow subgroup of some S-quasinormal subgroup of G. In this paper, we are interested in studying the structure of the finite group G under the assumption that certain subgroups of prime power order of G are s-semipermutable or S-quasinormally embedded in G. Some recent results are improved and generalized.

In this paper, we investigate the structure of a finite group G under the assumption that certain... more In this paper, we investigate the structure of a finite group G under the assumption that certain abelian subgroups of largest possible exponent of prime power order lie in the generalized hypercenter of the group G , and some known results on supersolvability of finite groups are generalized.

Discrete Mathematics, 2016

Cyclic isodual codes over F q are constructed in length ? 2 ( mod 4 ) , for odd q , and in length... more Cyclic isodual codes over F q are constructed in length ? 2 ( mod 4 ) , for odd q , and in length ? 4 ( mod 8 ) , for q ? 1 ( mod 4 ) . Their minimum distance is computed in short lengths.

Designs, Codes and Cryptography, 2015

The even-weight subcode of a binary Zetterberg code is a cyclic code with generator polynomial g(... more The even-weight subcode of a binary Zetterberg code is a cyclic code with generator polynomial g(x) = (x + 1) p(x), where p(x) is the minimum polynomial over G F(2) of an element of order 2 m + 1 in G F(2 2m) and m is even. This even binary code has parameters [2 m + 1, 2 m − 2m, 6]. The quaternary code obtained by lifting the code to the alphabet Z 4 = {0, 1, 2, 3} is shown to have parameters [2 m + 1, 2 m − 2m, d L ], where d L ≥ 8 denotes the minimum Lee distance. The image of the Gray map of the lifted code is a binary code with parameters (2 m+1 + 2, 2 k , d H), where d H ≥ 8 denotes the minimum Hamming weight and k = 2 m+1 − 4m. For m = 6 these parameters equal the parameters of the best known binary linear code for this length and dimension. Furthermore, a simple algebraic decoding algorithm is presented for these Z 4-codes for all even m. This appears to be the first infinite family of Z 4-codes of length n = 2 m + 1 with d L ≥ 8 having an algebraic decoding algorithm. Keywords Zetterberg code • Cyclic codes • Codes over Z 4 Mathematics Subject Classification 94B15 • 94B35 1 Introduction Codes over Z 4 , the ring of integers modulo 4, have been intensively studied during the last 25 years using the theory of Galois rings, in particular after the ideas developed in the 1990s Communicated by J. Bierbrauer.

Cryptography and Communications, 2015

The binary Melas code is a cyclic code with generator polynomial g(u) = p(u)p(u) * where p(u) is ... more The binary Melas code is a cyclic code with generator polynomial g(u) = p(u)p(u) * where p(u) is a primitive polynomial of odd degree m ≥ 5 and the * denotes reciprocation. The even-weight subcode of a Melas code has generator polynomial (u + 1)g(u) and parameters [2 m − 1, 2 m − 2m − 2, 6]. This code is lifted to Z 4 and the quaternary code is shown to have parameters [2 m − 1, 2 m − 2m − 2, d L ≥ 8], where d L denotes the minimum Lee distance. An algebraic decoding algorithm correcting all errors of Lee weight ≤ 3 is presented for this code. The Gray map of this quaternary code is a binary code with parameters [2 m+1 − 2, 2 m+1 − 4m − 4, d H ≥ 8] where d H is the minimum Hamming distance. For m = 5, 7 the minimum distance equals the minimum distance of the best known linear code for the given length and code size.

... INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS AXIOMATIC CHARACTERIZATION OF THE ALEXANDER-SPAN... more ... INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS AXIOMATIC CHARACTERIZATION OF THE ALEXANDER-SPANIER K-TYPES ... such that gτ EG&#x27; for each τ E f(g). 1 Alexander-Spanier Cohomology K -Types Let C9(r) (X) be the group of all functions tpT : Xg(r)+1 ...

Acta Mathematica Hungarica, 2012

We say that the subgroups G1 and G2 of a group G are mutually permutable if G1 permutes with ever... more We say that the subgroups G1 and G2 of a group G are mutually permutable if G1 permutes with every subgroup of G2 and G2 permutes with every subgroup of G1. Let G = G1G2. .. Gn be the product of its pairwise permutable subgroups G1, G2,. .. , Gn such that the product GiGj is mutually permutable. We investigate the structure of the finite group G if special properties of the factors G1, G2,. .. , Gn are known. Our results improve and extend some results of Asaad and Shaalan [1], Ezquerro and Soler-Escrivà [9] and Asaad and Monakhov [3].

Acta Mathematica Scientia, 2012

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H)∩H g ≤ H for all ... more Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H)∩H g ≤ H for all g ∈ G. A subgroup H of G is called a weakly H *-subgroup in G if there exists a subgroup K of G such that G = HK and H ∩ K is an H-subgroup in G. We investigate the structure of the finite group G under the assumption that every cyclic subgroup of G of prime order p or of order 4 (if p = 2) is a weakly H *-subgroup in G. Our results improve and extend a series of recent results in the literature. following concept: A subgroup H of a group G is called c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ H G. Also, in 2000, Bianchi et al. [4] introduced the concept of an H-subgroup as follows: A subgroup H of a group G is called an H-subgroup if N G (H) ∩ H g ≤ H for all g ∈ G. Recently, in 2012, Asaad, Heliel and Al-Shomrani [2] introduced a new concept, called a weakly H-subgroup, as follows: A subgroup H of a group G is called a weakly H-subgroup in G if there