Finite groups with few subgroups not in the Chermak–Delgado lattice

Q: What type of study is this?

This is a Quantitative Study study.

Jiaying Lu; Xi Huang; Qinwei Lian; Wei Meng

doi:10.1515/jgth-2025-0065

October 10, 2025Journal of Group Theory

Finite groups with few subgroups not in the Chermak–Delgado lattice

View at Publisher

Ask AI

Bookmark

Share

Key Points

Finite groups are characterized by having 1, 2, or 3 conjugacy classes of subgroups not in the Chermak–Delgado lattice.
The number of such unique subgroup configurations highlights distinct structural properties within group theory.
This assessment employs a classification approach to systematically ascertain the subgroups' characteristics.
Results indicate that specific configurations of finite groups bear significant implications for understanding subgroup relationships.

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

This research identifies finite groups with specific subgroup counts, revealing implications for group theory.

Abstract

For a finite group 𝐺, we denote by <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="script">C</m:mi> <m:mo>⁢</m:mo> <m:mi mathvariant="script">D</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> CD(G) the Chermak–Delgado lattice of 𝐺, and by <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>v</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> v(G) the number of conjugacy classes of subgroups of 𝐺 not in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="script">C</m:mi> <m:mo>⁢</m:mo> <m:mi mathvariant="script">D</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> CD(G) . In this paper, we determine the finite groups 𝐺 for which <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi>v</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mn>3</m:mn> </m:mrow> </m:mrow> </m:math> v(G)=1,2,3 .

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Lu et al. (2025) studied this question.

synapsesocial.com/papers/68ec384042a190b2c3519788 https://doi.org/10.1515/jgth-2025-0065

View at Publisher

Ask AI

Bookmark

Share

Finite groups with few subgroups not in the Chermak–Delgado lattice

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Finite groups with few subgroups not in the Chermak–Delgado lattice

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading