Finite groups whose minimal subgroups are weakly H*-subgroups

• Main Authors: Abdelrahman Abdelhamid Heliel, Rola Asaad Hijazi, Reem Abdulaziz Al-Obidy
• Format: Article
• Language: English
• Published: University of Isfahan 2014-09-01
• Series: International Journal of Group Theory
• Subjects: weakly H-subgroup; weakly H^{∗}-subgroup; c-supplemented subgroup; generalized Fitting subgroup
• Online Access: http://www.theoryofgroups.ir/pdf_3837_4ba7139afccee4a6543ffa5a60f76f6d.html

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if N_{G}(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.