Finite p−groups with small number of degrees of irreducible character

Let G be a finite p−group with cd(G) = {1, p^m}. In this paper, we prove that the order of the commutator subgroup satisfies |G| ≥ p^{(n−2)m+1} if m ≥ 2 and the nilpotent class c(G) = n. We also classify the finite p−group G with G′ cyclic and the nilpotent class c(G) = 2.

Authors

Heng Lv (ORCID: https://orcid.org/0000-0003-2103-4915)
Liangcai Zhang
Haibo Xue

Institutions

Southwest University (CN)
Chongqing University (CN)
Chongqing University of Science and Technology (CN)
Chongqing University of Technology (CN)

Publication Details

Journal: Hacettepe Journal of Mathematics and Statistics
Published: 2025-12-30
DOI: https://doi.org/10.15672/hujms.1781221
Primary Topic: Finite Group Theory Research
Type: article
Field-Weighted Citation Impact: 0.00

Funders

National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities

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article

Finite p−groups with small number of degrees of irreducible character

Heng Lv, Liangcai Zhang, Haibo Xue

Dec 30, 2025

Hacettepe Journal of Mathematics and Statistics

Finite Group Theory Research

article

Finite p−groups with small number of degrees of irreducible character

Heng Lv, Liangcai Zhang, Haibo Xue

December 30, 2025article en

Abstract

Let G be a finite p−group with cd(G) = {1, p^m}. In this paper, we prove that the order of the commutator subgroup satisfies |G| ≥ p^{(n−2)m+1} if m ≥ 2 and the nilpotent class c(G) = n. We also classify the finite p−group G with G′ cyclic and the nilpotent class c(G) = 2.

Hacettepe Journal of Mathematics and Statistics(Advanced Online Publication)

Southwest University (CN), Chongqing University (CN), Chongqing University of Science and Technology (CN), Chongqing University of Technology (CN)

National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Openalex Percentile: Top 17%

Finite Group Theory Research

DOI Open Access PDF OpenAlex

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