CLTσ-group with σ-subnormal or Self-normalizing Subgroups

Let G be a finite group and σ = { σ i ∣ i ⋃ I } be a partition of the set of all primes ℙ, that is, ℙ = ∪ i ∈ I σ i and σ i ∩ σ j = ∅ for all i ≠ j . A set ℋ of subgroups of G is said to be a complete Hall σ -set of G if every non-identity member of ℋ is a Hall σ i -subgroup of G for some i and ℋ co...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Frontiers of Mathematics 2023-07, Vol.18 (4), p.961-975
Hauptverfasser: Wu, Zhenfeng, Yang, Nanying
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Let G be a finite group and σ = { σ i ∣ i ⋃ I } be a partition of the set of all primes ℙ, that is, ℙ = ∪ i ∈ I σ i and σ i ∩ σ j = ∅ for all i ≠ j . A set ℋ of subgroups of G is said to be a complete Hall σ -set of G if every non-identity member of ℋ is a Hall σ i -subgroup of G for some i and ℋ contains exactly one Hall σ i -subgroup of G for every σ i ∈ σ ( G ). A group G is said to be a CLT σ -group if G has a complete Hall σ -set { H 1 , …, H t } such that for all subgroups A i ≤ H i , G has a subgroup of order ∣ A 1 ∣ … ∣ A t ∣. A group G is a generalized CLT σ -group, if G has a complete Hall σ -set { H 1 , …, H t } such that for all subgroups A i ≤ H i , G has a subgroup A of order ∣ A 1 ∣ … ∣ A t ∣ such that A satisfies some σ -normality condition. In this paper, we study the generalized CLT σ -groups which are characterized completely under some conditions.
ISSN:2731-8648
1673-3452
2731-8656
1673-3576
DOI:10.1007/s11464-020-0126-8