A `transversal' for minimal invariant sets in the boundary of a CAT(0) group

Structures induced on transversals to a subgroup of a group and hypergroups over the group

On the transversals of a subgroup of a group, using the binary operation of the group, structural mappings are defined. Based on these mappings, the notion of the hypergroup over the group is introduced, which generalizes the notion of the quotient-group of the given group with respect to the normal subgroup. The category of the hypergroups over the group contains as subcategories the category of groups, the category of linear spaces, the category of fields.

自由群代数中的暴露序：极小Schreier横截、自由基与Gröbner基

Exposure Orders in Free Group Algebras: Minimal Schreier Transversals, Free Bases, and Gröbner Bases

本文证明自由群代数中每个单侧理想在暴露序下存在极小Schreier横截、基和Gröbner基，并给出有限生成情形下的算法，推广了Lewin和Rosenmann的工作。

Investigating transversals as generating sets for groups

In [3] is was shown that for any group $G$ whose rank (i.e., minimal number of generators) is at most 3, and any finite index subgroup $H\leq G$ with index $[G:H]\geq rank(G)$, one can always find a left-right transversal of $H$ which generates $G$. In this paper we extend this result to groups of rank at most 4. We also extend this to groups $G$ of arbitrary (finite) rank $r$ provided all the non-trivial divisors of $[G:core_G(H)]$ are at least $2r-1$. Finally, we extend this to groups $G$ of arbitrary (finite) rank provided $H$ is malnormal in $G$.

CAT(0)立方复形中的最小位移集

Minimal displacement set for CAT(0) cubical complexes

本文研究CAT(0)立方复形中最小位移集的结构，证明其凸性、局部CAT(0)度量性和单连通性。