Lijian An

activity

20132025

p

-groups with a minimal non-abelian subgroup of index

p

(IV)

24 citations · 34 across the 12 of their papers we have counts for

collaborators

12 papers

math.GR2025

Finite groups with the most Chermak-Delgado measures of subgroups

Guojie Liu, Haipeng Qu, Lijian An

Let $G$ be a finite group and $H \leq G$ . The Chermak-Delgado measure of $H$ is defined as the number $∣ H ∣ \cdot ∣ C_{G} (H) ∣$ . In this paper, we identify finite groups that exhibit the…

math.GR2023

On quadratic conjecture

Jingjing Duan, Lijian An

Quadratic conjecture is a strengthening of oliver's $p$ -group conjecture. Let $G$ be a $p$ -group of maximal class of order $p^{n}$ . We prove that if $n \leq 8$ or $n\ge \max\{2p-6,p+2\…

math.GR2023

Finite p-groups with at most p2 + p subgroups not in Chermak-Delgado lattice

Guojie Liu, Haipeng Qu, Lijian An

The Chermak-Delgado lattice of a finite group G is a self-dual sublattice of the subgroup lattice of G. In this paper, we determine finite p-groups with at most p2 + p subgroups no…

math.GR2021★ 2 cited

Groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian $p$ -group

Lijian An

The Chermak-Delgado lattice of a finite group $G$ is a self-dual sublattice of the subgroup lattice of $G$ . In this paper, we focus on finite groups whose Chermak-Delgado lattice i…

math.GR2021

Finite groups which have maximal covers

Lifang Wang, Lijian An

Let $λ (G)$ be the maximum number of subgroups in an irredundant covering of a finite group $G$ . We prove that the finite groups with $λ (G) = ∣ G ∣ - t$ , where $t \leq 5$ , are solvable, an…

math.GR2020

A refinement on a theorem of Z. Janko

Qiangwei Song, Lijian An

We say that a subgroup $H$ is isolated in a group $G$ if for each $x \in G$ we have either $x \in H$ or $⟨ x ⟩ \cap H = 1$ . Z. Janko, in his paper [J. Algebra, 465(2016),…

math.GR2017★ 1 cited

Groups whose Chermak-Delgado lattice is a quasi-antichain

Lijian An

A quasiantichain is a lattice consisting of a maximum, a minimum, and the atoms of the lattice. The width of a quasiantichian is the number of atoms. For a positive integer $w$ ($\…

math.GR2014★ 2 cited

On Finite Metahamiltonian p-Groups

Lijian An, Qinhai Zhang

A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generalization of Hamiltonian groups. In this paper, the properties of fi…

math.GR2013

Finite $p$ -groups with a minimal non-abelian subgroup of index $p$ (III)

Haipeng Qu, Mingyao Xu, Lijian An

In this paper, we finished the classification of three-generator finite $p$ -groups $G$ such that $Φ (G) \leq Z (G)$ . This paper is a part of classification of finite $p$ -groups with a…

math.GR2013★ 5 cited

The Classification of Finite Metahamiltonian $p$ -Groups

Xingui Fang, Lijian An

A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generation of Hamiltonian groups. In this paper, a complete classificatio…

math.GR2013★ 24 cited

Finite $p$ -groups with a minimal non-abelian subgroup of index $p$ (IV)

Lijian An, Ruifang Hu, Qinhai Zhang

In this paper, we completely classify the finite $p$ -groups $G$ such that $Φ (G^{'}) G_{3} \leq C_{p}^{2}$ , $Φ (G^{'}) G_{3} \leq Z (G)$ and $G /Φ (G^{'}) G_{3}$ is minimal non-abelian. This paper is a part of t…

math.GR2013

Chermak-Delgado Lattice Extension Theorems

Lijian An, Joseph Brennan, Haipeng Qu +1

In a finite group G with subgroup H, the Chermak-Delgado measure of H (in G) is defined as the product of the order of H with the order of the centralizer of H. The Chermak-Delgado…

Finite groups with the most Chermak-Delgado measures of subgroups

On quadratic conjecture

Finite p-groups with at most p2 + p subgroups not in Chermak-Delgado lattice

Groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian p-group

Finite groups which have maximal covers

A refinement on a theorem of Z. Janko

Groups whose Chermak-Delgado lattice is a quasi-antichain

On Finite Metahamiltonian p-Groups

Finite p-groups with a minimal non-abelian subgroup of index p (III)

The Classification of Finite Metahamiltonian p-Groups

Finite p-groups with a minimal non-abelian subgroup of index p (IV)

Chermak-Delgado Lattice Extension Theorems

Groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian $p$ -group

Finite $p$ -groups with a minimal non-abelian subgroup of index $p$ (III)

The Classification of Finite Metahamiltonian $p$ -Groups

Finite $p$ -groups with a minimal non-abelian subgroup of index $p$ (IV)