A remark on thickness of free-by-cyclic groups

Some remarks on cyclic Galois coverings of the projective line over finite fields

We study cyclic finite Galois extensions of the rational function field of the projective line P^{1}(F_q) over a finite field F_q with q elements defined by considering quotient curves by finite subgroups of the projective linear group PGL(2,q), and we enumerate them expressing the count in terms of Stirling numbers.

A remark on {2,3}-groups with no elements of order six

We describe $\{2,3\}$-groups in which the order of a product of any two elements of orders at most $4$ does not exceed $9$ and the centralizer of every involution is a locally cyclic $2$-subgroup. In particular, we will prove that these groups are locally finite.

A Remark on Generalized Covering Groups

Let ${\cal N}_c$ be the variety of nilpotent groups of class at most $c\ \ (c\geq 2)$ and $G=Z_r\oplus Z_s $ be the direct sum of two finite cyclic groups. It is shown that if the greatest common divisor of $r$ and $s$ is not one, then $G$ does not have any ${\cal N}_c$-covering group for every $c\geq 2$. This result gives an idea that Lemma 2 of J.Wiegold [6] and Haebich's Theorem [1], a vast generalization of the Wiegold's Theorem, can {\it not} be generalized to the variety of nilpotent groups of class at most $c\geq 2$.

关于自由循环群和管状群的一些问题

Some questions related to free-by-cyclic groups and tubular groups

本文研究自由循环管状群的特殊性、虚拟作用及循环子群可分离性，否定多个相关猜想并提供反例。

Thurston 范数、多面体与分裂复杂度

Thurston norm, polytopes and splitting complexity

研究满足强Atiyah猜想的无挠群，将核的第一L²-Betti数延拓为Thurston半范数，证明其由同调群中的多面体诱导，并推广到高阶L²-Betti数；在自由-循环群和三维流形基本群情形给出组合解释，应用于计算BNS不变量。