On p-nilpotency of finite groups?

2013/08/02 by Baojun Li, Li, Baojun, Tuval Foguel +1
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1308.0408

Abstract

Let H be a subgroup of a group G. H is said satisfying Π-property in G, if |G/K:N_G/K(HK/K∩ L/K)| is a π(HK/K∩ L/K))-number for any chief factor L/K of G, and, if there is a subnormal supplement T of H in G such that H∩ T≤ I≤ H for some subgroup I satisfying Π-property in G, then H is said Π-normal in G. By these properties of some subgroups, we obtain some new criterions of p-nilpotency of finite groups.

Related

• A note on the Π-property of some subgroups of finite groups
• On Π-supplemented subgroups of a finite group
• On the IC-Π-property of subgroups of finite groups
• On the partial \mathscr L - Π-property of subgroups of finite groups
• Finite groups with some subgroups satisfying the partial Π-property