SΦ-supplemented subgroups of finite groups

• Published in: Український математичний журнал
• Date: 2012
• ISSN: 1027-3190
• Main Authors: Xianhua Li, Tao Zhao
• Format: Article
• Language: English
• Published: Український математичний журнал 2012
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164160
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: SΦ-supplemented subgroups of finite groups / Xianhua Li, Tao Zhao // Український математичний журнал. — 2012. — Т. 64, № 1. — С. 92-99. — Бібліогр.: 13 назв. — англ.

We call H an SΦ-supplemented subgroup of a finite group G if there exists a subnormal subgroup T of G such that G = HT and H ∩ T ≤ Φ(H), where Φ(H) is the Frattini subgroup of H. In this paper, we characterize the p-nilpotency and supersolubility of a finite group G under the assumption that every s...