Subgroup theorem for valuated groups and the CSA property

On CT and CSA Groups and Related Ideas

A group is $G$ commutative transitive or CT if commuting is transitive on nontrivial elements. A group $G$ is CSA or conjugately separated abelian if maximal abelian subgroups are malnormal. These concepts have played a prominent role in the studies of fully residually free groups, limit groups and dicriminating groups. They were especially important in the solution to the Tarski problems. CSA always implies CT however the class of CSA groups is a proper subclass of the class of CT groups. For limit groups and finitely generated elementary free groups they are equivalent. In this paper we exam…

CSA groups and separated free constructions

A group $G$ is said to be a {\it CSA}-group if all maximal abelian subgroups of $G$ are malnormal. The class of CSA groups is of interest because it contains torsion-free hyperbolic groups, groups acting freely on $Λ$-trees and groups with the same existential theory as free groups. CSA groups are also very closely related to the study of residually free groups and tensor completions. In this paper we investigate which free constructions (amalgamated products and HNN extensions) over CSA groups are again CSA. The results are applied, in particular, to show that a torsion-free one-relator group…

关于幂零子群的共轭可分性

On conjugate separability of nilpotent subgroups

本文研究所有类至多为 k 的极大幂零子群均畸正规的群，证明其与 CSA 群性质相似，并引入幂零传递群，在特定剩余条件下证明两者等价，从而将 CSA 与 CT 群理论纳入更一般的框架。

作为方程定义域的新群类

New classes of groups which are equational domains

该研究推广了非阿贝尔CSA群为方程定义域的结论，从k类幂零子群极大元非正规、极大局部幂零子群非正规两个方向，给出了非幂零/非局部幂零群成为方程定义域的新条件。

Embeddings and chains of free groups

We build two non-abelian CSA-groups in which maximal abelian subgroups are conjugate and divisible.

有限群的交图直径

On the diameter of intersection graphs of finite groups

本文回答了 Csákány 和 Pollák 关于有限群交图直径的两个长期未解问题，给出了非单群交图直径为 4 的必要条件，并首次构造了直径为 4 的非单群和交错群实例。