Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup

Shi, Jiangtao; Zhang, Cui

doi:10.1007/s00013-013-0545-9

Arch. Math.

2013

DOI: 10.1007/s00013-013-0545-9

|View full text |Cite

Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup

Jiangtao Shi

Cui Zhang

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

2024

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 9 publications

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Finite Groups All of Whose Subgroups are $$\mathbb {P}$$-Subnormal or $${{\,\textrm{TI}\,}}$$-Subgroups

Ballester-Bolinches,

Kamornikov,

Pérez-Calabuig

et al. 2024

Mediterr. J. Math.

View full text Add to dashboard Cite

Let $$\mathbb {P}$$ P be the set of all prime numbers. A subgroup H of a finite group G is said to be $$\mathbb {P}$$ P -subnormal in G if there exists a chain of subgroups $$\begin{aligned} H = H_0 \subseteq H_1 \subseteq \cdots \subseteq H_{n-1} \subseteq H_n = G \end{aligned}$$ H = H 0 ⊆ H 1 ⊆ ⋯ ⊆ H n - 1 ⊆ H n = G such that either $$H_{i-1}$$ H i - 1 is normal in $$H_i$$ H i or $$|H_i{:}\, H_{i-1}|$$ | H i : H i - 1 | is a prime number for every $$i = 1, 2, \ldots , n$$ i = 1 , 2 , … , n . A subgroup H of G is called a $${{\,\textrm{TI}\,}}$$ TI -subgroup if every pair of distinct conjugates of H has trivial intersection. The aim of this paper is to give a complete description of all finite groups in which every non-$$\mathbb {P}$$ P -subnormal subgroup is a $${{\,\textrm{TI}\,}}$$ TI -subgroup.

show abstract

Finite Groups All of Whose Subgroups are $$\mathbb {P}$$-Subnormal or $${{\,\textrm{TI}\,}}$$-Subgroups

Ballester-Bolinches,

Kamornikov,

Pérez-Calabuig

et al. 2024

Mediterr. J. Math.

View full text Add to dashboard Cite

show abstract

Finite simple groups the nilpotent residuals of all of whose subgroups are TI-subgroups

Meng

Zhang

2023

Ricerche mat

View full text Add to dashboard Cite

Finite groups whose non-σ-subnormal subgroups are TI-subgroups

Wang

Kamornikov

2023

Communications in Algebra

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup

Cited by 9 publications

References 5 publications

Finite Groups All of Whose Subgroups are $$\mathbb {P}$$-Subnormal or $${{\,\textrm{TI}\,}}$$-Subgroups

Finite Groups All of Whose Subgroups are $$\mathbb {P}$$-Subnormal or $${{\,\textrm{TI}\,}}$$-Subgroups

Finite simple groups the nilpotent residuals of all of whose subgroups are TI-subgroups

Finite groups whose non-σ-subnormal subgroups are TI-subgroups

Contact Info

Product

Resources

About