P-Hypercyclically embedding and Π-property of subgroups of finite groups. Issue 8 (3rd August 2017)

• Record Type: Journal Article
• Authors: Li, Yangming; Miao, Liyun
• Is Part Of: Communications in algebra. Volume 45:Issue 8(2017)
• Page Start: 3468
• Page End: 3474
• Publication Date: 2017-08-03
• Subjects: p-Hypercyclically embedded subgroup -- Π-normality -- Π-property -- Π*-property; 20D10 -- 20D15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1236939
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let G be a finite group, E a normal subgroup of G and p a fixed prime. We say that E is p-hypercyclically embedded in G if every p - G -chief factor of E is cyclic. A subgroup H of G is said to satisfy Π- property in G if | G ∕ K : N G ∕ K (( H ∩ L ) K ∕ K )| is a π (( H ∩ L ) K ∕ K )-number for any chief factor L ∕ K in G ; we say that H has Π*-property in G if H ∩ O π ( H ) ( G ) has Π-property in G . In this paper, we prove that E is p -hypercyclically embedded in G if and only if some classes of p -subgroups of E have Π*-property in G . Some recent results are extended.