3 papers
math.GR2026
Commutator relators of one-relator groups do not force Hopficity, residual finiteness, or automaticity
Ke Wang, Qiang Zhang
Let be a one-relator group with the relator or , where is a finitely generated free group. Baumslag asked…
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…