The Criterion of Shmel'kin and Varieties Generated by Wreath Products of Finite Groups

关于Shmel'kin定理的一个推广

On a generalization of Shmel'kin's theorem

研究周期幂零群和无挠幂零群是否包含所有无限单模方程组在自身上的解，推广了已知的有限情形结论。

群的言语积与言语圈积的永久性性质

Permanence properties of verbal products and verbal wreath products of groups

本文研究群的言语积与言语圈积，证明sofic性、Haagerup性质等多项性质在幂零积等操作下得以保持，并应用于自由群的商。

On varieties of groups in which all periodic groups are abelian

To solve a number of problems on varieties of groups, stated by Kleiman, Kuznetsov, Ol'shanskii, Shmel'kin in the 1970's and 1980's, we construct continuously many varieties of groups in which all periodic groups are abelian and whose pairwise intersections are the variety of all abelian groups.

无限循环顶群的圈积的交换度

The degree of commutativity of wreath products with infinite cyclic top group

本文证明对形如$H \wr \langle t \rangle$（顶群无限循环）的受限圈积，无论生成集如何选择，其交换度恒为零，推广了Cox关于灯架群的结果，并给出了基群像密度为零的推广结论。

类灯群的分析、几何与度量方面

Analytic, geometric and measured aspects of lamplighter-like groups

本论文从拟等距与度量角度研究类灯群，给出置换圈积的拟等距分类及刚性结果，并构造晕积的轨道等价耦合，改进等周轮廓估计。

Some Groups with Computable Chermak-Delgado Lattices

Let G be a finite group and let H be a subgroup of G. The Chermak-Delgado measure of H with respect to G is the product of the order of H with the order of the centralizer of H. Originally described by A. Chermak and A. Delgado, the collection of all subgroups of G with maximal Chermak-Delgado measure, denoted CD(G), is a sublattice of the lattice of all subgroups of G. In this paper we note that the members of CD(G) are subnormal in G and determine the Chermak-Delgado lattice of direct products. We additionally describe the lattice for certain kinds of wreath products and examine the behavior…