Binzhou Xia

activity

20242026

collaborators

8 papers

math.GR2026

Almost all finite groups are $2$ -groups of class two

Ning Su, Binzhou Xia

We prove that almost all finite groups are $2$ -groups of nilpotency class two, when groups of order at most $x$ are counted up to isomorphism and $x \to \infty$ . More precisely, unif…

math.GR2026

Automorphism groups of Cayley graphs on almost simple groups with normal connection sets

Mengyu Cao, Benjian Lv, Binzhou Xia

We determine the full automorphism group of every connected Cayley graph on an almost simple group with a normal connection set. We also characterize exactly when the full automorp…

math.GR2026

Solvable Supplements to Normalizers of Cyclic 2-Subgroups

Shou Hong Qiao, Binzhou Xia

Amberg and Kazarin proved that a finite group is solvable if the normalizer of every cyclic subgroup of prime power order has a solvable supplement. We substantially relax this hyp…

math.CO2025

Which maximal subgroups are perfect codes?

Shouhong Qiao, Ning Su, Binzhou Xia +2

A perfect code in a graph $Γ = (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V ∖ C$ is adjacent to exactly one vertex in $…

math.CO2025

Determining the vertex stabilizers of 4-valent half-arc-transitive graphs

Binzhou Xia, Zhishuo Zhang, Sanming Zhou

We say that a group is a $4$ -HAT-stabilizer if it is the vertex stabilizer of some connected $4$ -valent half-arc-transitive graph. In 2001, Marušič and Nedela proved that every $4$ …

math.CO2025

On subgroup perfect codes in vertex-transitive graphs

Binzhou Xia, Junyang Zhang, Zhishuo Zhang

A subset $C$ of the vertex set $V$ of a graph $Γ$ is called a perfect code in $Γ$ if every vertex in $V ∖ C$ is adjacent to exactly one vertex in $C$ . Given a group $G$ and…

math.GR2024

On biprimitive semisymmetric graphs

Yunsong Gan, Weijun Liu, Binzhou Xia

A regular bipartite graph $Γ$ is called semisymmetric if its full automorphism group $Aut (Γ)$ acts transitively on the edge set but not on the vertex set. For a subgroup $…

math.CO2024

Asymptotic enumeration of Haar graphical representations

Yunsong Gan, Pablo Spiga, Binzhou Xia

This paper represents a significant leap forward in the problem of enumerating vertex-transitive graphs. Recent breakthroughs on symmetry of Cayley (di)graphs show that almost all…

Almost all finite groups are 2-groups of class two

Automorphism groups of Cayley graphs on almost simple groups with normal connection sets

Solvable Supplements to Normalizers of Cyclic 2-Subgroups

Which maximal subgroups are perfect codes?

Determining the vertex stabilizers of 4-valent half-arc-transitive graphs

On subgroup perfect codes in vertex-transitive graphs

On biprimitive semisymmetric graphs

Asymptotic enumeration of Haar graphical representations

Almost all finite groups are $2$ -groups of class two