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 $π_{1} (Σ_{g}) = ⟨ c_{1}, \dots, c_{2 g} ∣ c_{1} \dots c_{2 g} c_{1}^{- 1} \dots c_{2 g}^{- 1} ⟩$ with genus $g \geq 2$ , we provide an explicit bound $n-1\leq \mathrm{…

math.GT2025

Word Length Formulae, Normal Forms, Conjugation and Root-finding Algorithms in Surface Groups

Ke Wang, Qiang Zhang, Xuezhi Zhao

In this paper, we mainly study the following symmetric presentation of the surface group $$π_1(Σ_g)=\left\langle c_1,\dots, c_{2g}\mid c_1\cdots c_{2g}c_1^{-1}\cdots c_{2g}^{-1}\ri…

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…