On 𝔉-radicals of finite π-soluble groups

• Published in: Algebra and Discrete Mathematics
• Date: 2006
• Main Authors: Guo, W., Xi Liu, Baojun Li
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2006
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/157379
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On 𝔉-radicals of finite π-soluble groups / W. Guo, Xi Liu, Baojun Li // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 49–54. — Бібліогр.: 7 назв. — англ.

In this paper, we prove that for every local πsaturated Fitting class 𝔉 with char(𝔉) = P, the F-radical of every finite π-soluble groups G has the property: CG(G𝔉 ) ⊆ G𝔉 . From this, some well known results are followed and some new results are obtained.