Cover-avoidance properties and the structure of finite groups

✍ Scribed by Guo Xiuyun; K.P. Shum

• Book ID: 104152641
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 137 KB
• Volume: 181
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(02)00327-4

✦ Synopsis

We call a subgroup A of a ÿnite group G a CAP-subgroup of G if for any chief factor H=K of G, we have H ∩ A = K ∩ A or HA = KA. In this paper, some characterizations for a ÿnite group to be solvable are obtained under the assumption that some of its maximal subgroups or 2-maximal subgroups be CAP-subgroups. We also determine the p-solvability and p-nilpotency of ÿnite groups by considering their CAP-subgroups.