Mohamed Asaad

A subgroup of a group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be S-quasinormally embedded in G if for each prime p dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G. In this paper we investigate the influence of S-quasinormally embedded of some subgroups of prime power order on the structure of finite groups. Our results improve and extend recent results of Ballester-Bolinches and Pedraza-Aguilera (J. Pure Appl. Algebra 127 (1998) 113).

A subgroup of a group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be S-quasinormally embedded in G if for each prime p dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G. In this paper we investigate the influence of S-quasinormally embedded of some subgroups of prime power order on the structure of finite groups. Our results improve and extend recent results of Ballester-Bolinches and Pedraza-Aguilera (J. Pure Appl. Algebra 127 (1998) 113).

This paper is a continuation of our earlier work (Abou-Zaid, 1991, 1992; Asaad 1991; Asaad and Abou-Zaid, 1993, 1995) in order to investigate further the problem given by Asaad (1991): What can be said about the structure of a fuzzy subgroup A of a group G when information is available about the structure of G and vice versa?

In this paper we continue our study in order to give a partial answer to the question suggested by Asaad in 1991: What can be said about the structure of a group G when the information are known about the structure of a fuzzy subgroup A of G and viceversa?