On the partial Π-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

Let H be a subgroup of a finite group G. We say that H satisfies the partial Π -property in G if there exists a chief series Γ G : 1 = G 0 < G 1 < · · · < G n = G of G such that for every G-chief factor G i / G i − 1 ( 1 ≤ i ≤ n ) of Γ G ,   | G / G i − 1 : N G / G i − 1 ( H G i − 1 / G i −...

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Bibliographic Details
Published in:Communications in algebra 2024-12, Vol.52 (12), p.5203-5214
Main Authors: Qiu, Zhengtian, Chen, Guiyun, Liu, Jianjun
Format: Article
Language:English
Subjects:
Finite group
Group theory
p-length
p-soluble group
property
Subgroups
the partial
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Summary:Let H be a subgroup of a finite group G. We say that H satisfies the partial Π -property in G if there exists a chief series Γ G : 1 = G 0 < G 1 < · · · < G n = G of G such that for every G-chief factor G i / G i − 1 ( 1 ≤ i ≤ n ) of Γ G ,   | G / G i − 1 : N G / G i − 1 ( H G i − 1 / G i − 1 ∩ G i / G i − 1 ) | is a π ( H G i − 1 / G i − 1 ∩ G i / G i − 1 ) -number. In this paper, we study the influence of some second minimal or second maximal subgroups of a Sylow subgroup satisfying the partial Π -property on the structure of a finite group.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2367169