Counting $(1,β)$-BM relations and classifying $(2,2)$-BM groups

Relations between counting functions on free groups and free monoids

We consider finite sums of counting functions on the free group $F_n$ and the free monoid $M_n$ for $n \geq 2$. Two such sums are considered equivalent if they differ by a bounded function. We find the complete set of linear relations between equivalence classes of sums of counting functions and apply this result to construct an explicit basis for the vector space of such equivalence classes. Moreover, we provide a graphical algorithm to determine whether two given sums of counting functions are equivalent. In particular, this yields an algorithm to decide whether two sums of Brooks quasimorph…

ZM-群的共轭类与自同构共轭类的计数

Counting conjugacy classes and automorphism-conjugacy classes of ZM-groups

本文研究ZM-群中元素的共轭类与自同构共轭类，给出了两类等价关系下的类数及各类大小的计数结果。

New collections of p-subgroups and homology decompositions for classifying spaces of finite groups

Let G be a finite group and p a prime dividing its order. We define new collections of p-subgroups of G. We study the homotopy relations among them and with the standard collections of p-subgroups. We determine their ampleness and sharpness properties.

对称群的一个分类空间的3-骨架

A 3-skeleton for a classifying space for the symmetric group

本文构造了对称群的 Eilenberg-MacLane 分类空间的 3-骨架，并利用重写系统与 K. Brown 方法验证其正确性，进而计算了扭曲系数下的第二上同调和未扭曲系数下的第三同调。

一种计算 $U_{6n}$ 中所有（正规）模糊子群数量的算法

An algorithm for counting number of all (normal) fuzzy subgroups in $U_{6n}$

本文基于 $U_{6n}$ 群子群结构的已知结果，提出一种动态规划算法，用于在特定等价关系下计算其所有正规模糊子群的数量。