Khaled Al-Sharo - Academia.edu (original) (raw)

Uploads

Papers by Khaled Al-Sharo

2021 International Conference on Information Technology (ICIT)

Bulletin of the Iranian Mathematical Society

Communications in Algebra, 2016

Journal of Group Theory, 2016

A subgroupOur main goal here is to prove the following result (Theorem 1.2):This theorem generali... more A subgroupOur main goal here is to prove the following result (Theorem 1.2):This theorem generalizes many known results and also gives the positive answer to Question 18.91 (b) in Kourovka Notebook [

ABSTRACT We study finite groups with generalized normality condition for subgroups of prime order.

Ricerche di Matematica, 2009

The class of groups G for which every subgroup of P ∈ Syl p (G) is normal (permutable) in N G (P)... more The class of groups G for which every subgroup of P ∈ Syl p (G) is normal (permutable) in N G (P) is called C p (X p). A finite solvable group possesses a transitive normality (permutability) relation if and only if it is a C p-group (X p-group) for all primes p. The classes T , PT , and PST denote, respectively, the classes of groups in which normality, permutability, and S-permutability are transitive relations. Our main result shows that the minimal non-C p-groups and the minimal non-X p-groups, respectively, are just the minimal non-T-groups and the minimal non-PT-groups. In addition, we arrive a new characterization of the solvable PT-groups and the solvable PST-groups.

Communications in Algebra, 2012

ABSTRACT Let G be a finite group and H ≤ G. The subgroup H is called: S-permutable in G if HP = P... more ABSTRACT Let G be a finite group and H ≤ G. The subgroup H is called: S-permutable in G if HP = PH for all Sylow subgroups P of G; S-permutably embedded in G if each Sylow subgroup of H is also a Sylow subgroup of some S-permutable subgroup of G.Let H be a subgroup of a group G. Then we say that H is SQ-supplemented in G if G has a subgroup T and an S-permutably embedded subgroup C ≤ H such that HT = G and T ∩ H ≤ C.We study the structure of G under the assumption that some subgroups of G are SQ-supplemented in G. Some known results are generalized.

Communications in Algebra, 2012

ABSTRACT We say that a subgroup H of a finite group G is nearly S-permutable in G if for every pr... more ABSTRACT We say that a subgroup H of a finite group G is nearly S-permutable in G if for every prime p such that (p, |H|) = 1 and for every subgroup K of G containing H the normalizer NK(H) contains some Sylow p-subgroup of K. We study the structure of G under the assumption that some subgroups of G are nearly S-permutable in G.

Acta Mathematica Hungarica, 2012

A subgroup H of G is c-permutable in G if there exists a permutable subgroup P of G such that HP=... more A subgroup H of G is c-permutable in G if there exists a permutable subgroup P of G such that HP=G and H∩P≦H pG , where H pG is the largest permutable subgroup of G contained in H. A group G is called CPT-group if c-permutability is transitive in G. A number of new characterizations of finite solvable CPT-groups are given.

Математические заметки, 2012

2021 International Conference on Information Technology (ICIT)

Bulletin of the Iranian Mathematical Society

Communications in Algebra, 2016

Journal of Group Theory, 2016

A subgroupOur main goal here is to prove the following result (Theorem 1.2):This theorem generali... more A subgroupOur main goal here is to prove the following result (Theorem 1.2):This theorem generalizes many known results and also gives the positive answer to Question 18.91 (b) in Kourovka Notebook [

ABSTRACT We study finite groups with generalized normality condition for subgroups of prime order.

Ricerche di Matematica, 2009

The class of groups G for which every subgroup of P ∈ Syl p (G) is normal (permutable) in N G (P)... more The class of groups G for which every subgroup of P ∈ Syl p (G) is normal (permutable) in N G (P) is called C p (X p). A finite solvable group possesses a transitive normality (permutability) relation if and only if it is a C p-group (X p-group) for all primes p. The classes T , PT , and PST denote, respectively, the classes of groups in which normality, permutability, and S-permutability are transitive relations. Our main result shows that the minimal non-C p-groups and the minimal non-X p-groups, respectively, are just the minimal non-T-groups and the minimal non-PT-groups. In addition, we arrive a new characterization of the solvable PT-groups and the solvable PST-groups.

Communications in Algebra, 2012

ABSTRACT Let G be a finite group and H ≤ G. The subgroup H is called: S-permutable in G if HP = P... more ABSTRACT Let G be a finite group and H ≤ G. The subgroup H is called: S-permutable in G if HP = PH for all Sylow subgroups P of G; S-permutably embedded in G if each Sylow subgroup of H is also a Sylow subgroup of some S-permutable subgroup of G.Let H be a subgroup of a group G. Then we say that H is SQ-supplemented in G if G has a subgroup T and an S-permutably embedded subgroup C ≤ H such that HT = G and T ∩ H ≤ C.We study the structure of G under the assumption that some subgroups of G are SQ-supplemented in G. Some known results are generalized.

Communications in Algebra, 2012

ABSTRACT We say that a subgroup H of a finite group G is nearly S-permutable in G if for every pr... more ABSTRACT We say that a subgroup H of a finite group G is nearly S-permutable in G if for every prime p such that (p, |H|) = 1 and for every subgroup K of G containing H the normalizer NK(H) contains some Sylow p-subgroup of K. We study the structure of G under the assumption that some subgroups of G are nearly S-permutable in G.

Acta Mathematica Hungarica, 2012

A subgroup H of G is c-permutable in G if there exists a permutable subgroup P of G such that HP=... more A subgroup H of G is c-permutable in G if there exists a permutable subgroup P of G such that HP=G and H∩P≦H pG , where H pG is the largest permutable subgroup of G contained in H. A group G is called CPT-group if c-permutability is transitive in G. A number of new characterizations of finite solvable CPT-groups are given.

Математические заметки, 2012