Ke Wang

collaborators

4 papers

math.GR2026

Commutator relators of one-relator groups do not force Hopficity, residual finiteness, or automaticity

Ke Wang, Qiang Zhang

Let $G = F / ⟨⟨ r ⟩⟩$ be a one-relator group with the relator $r \in [F, F]$ or $r = [u, v] (u, v \in F)$ , where $F$ is a finitely generated free group. Baumslag asked…

math.GR2026

An Explicit Bound for the Conjugator Length Function of a Surface Group

Ke Wang, Qiang Zhang

For a surface group $I ¨ _{1} (I^£_{g}) = ⟨ c_{1}, \dots, c_{2 g} ∣ c_{1} \dots c_{2 g} c_{1}^{- 1} \dots c_{2 g}^{- 1} ⟩$ with genus $g \geq 2$ , we provide an explicit bound $n-1\leq \mathr…

math.GT2025

Word Length Formulae and Normal Forms of Conjugacy Classes in Surface Groups

Ke Wang, Qiang Zhang, Xuezhi Zhao

In this paper, we primarily investigate the following symmetric presentation of the surface group $Ï_1(Î£_g)=\left\langle c_1,\dots, c_{2g}\mid c_1\cdots c_{2g}c_1^{-1}\cdots c_{2…

math.GR2025

Classification of Fixed Subgroups of Endomorphisms in Free-abelian Times Surface Groups

Ke Wang, Qiang Zhang, Dongxiao Zhao

In this paper, we first study the endomorphisms of free-abelian times surface groups and give a characterization of when they are injective and surjective. Then, we see that free-a…