On c-embedded subgroups of finite groups

2022/06/29 by Kaspczyk, Julian
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2206.14799

Abstract

Let G be a group and H ≤ K ≤ G. We say that H is c-embedded in G with respect to K if there is a subgroup B of G such that G = HB and H ∩ B ≤ Z(K). Given a finite group G, a prime number p and a Sylow p-subgroup P of G, we investigate the structure of G under the assumption that N_G(P) is p-supersolvable or p-nilpotent and that certain cyclic subgroups of P with order p or 4 are c-embedded in G with respect to P. New characterizations of p-supersolvability and p-nilpotence of finite groups will be obtained.

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