New characterizations of $$\sigma $$-nilpotent finite groups

Murashka, Viachaslau I.; Васильев, А. Ф.

doi:10.1007/s11587-021-00627-8

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The N-critical [23] graph Γ N c (G) of a group G is the directed graph whose vertex set coincides with π(G) such that (p, q) is an edge of Γ N c (G) whenever G contains a Schmidt (p, q)-subgroup. For its properties and applications see [16,18,23].…”

Section: Introductionmentioning

confidence: 99%

Arithmetic graphs and the products of finite groups

Murashka¹

2023

Preprint

View full text Add to dashboard Cite

The Hawkes graph Γ H (G) of G is the directed graph whose vertex set coincides with π(G) and it has the edge (p, q) whenever q ∈ π(G/O p ′ ,p (G)). The Sylow graph Γ s (G) of G is the directed graph with vertex set π(G) and (p, q) is an edge of Γ s (G) whenever q ∈ π(N G (P )/P C G (P )) for some Sylow p-subgroup P of G. The N -critical graph Γ N c (G) of a group G the directed graph whose vertex set coincides with π(G) such that (p, q) is an edge of Γ N c (G) whenever G contains a Schmidt (p, q)-subgroup, i.e. a Schmidt {p, q}-subgroup with a normal Sylow p-subgroup. In the paper the Hawkes, the Sylow and the N -critical graphs of the products of totally permutable, mutually permutable and N-connected subgroups are studied.

show abstract

Section: Introductionmentioning

confidence: 99%

Arithmetic graphs and the products of finite groups

Murashka¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

New characterizations of $$\sigma $$-nilpotent finite groups

Cited by 1 publication

References 21 publications

Arithmetic graphs and the products of finite groups

Arithmetic graphs and the products of finite groups

Contact Info

Product

Resources

About