A translation of G. S. Makanin's 1966 Ph.D. thesis "On the Identity Problem for Finitely Presented Groups and Semigroups"

自由群、半群、结合代数和李代数中元组集合的典范Makanin-Razborov图与伪拓扑 I

A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples in free groups, semigroups, associative algebras and Lie algebras I

本文提出统一方法将Makanin-Razborov图与自由群中元组集合关联，证明单端MR图存在典范图，并据此定义伪闭包、秩及典范包络以研究各类代数簇的全局结构。

字方程：对及其 Makanin-Razborov 图

Word Equations: Pairs and their Makanin-Razborov Diagrams

本文提出用于编码自由半群方程组解集的 Makanin-Razborov 图，并展示其可用于分析自由半群的一阶理论片段。

从代数构造拓扑

On constructing topology from algebra

本论文探讨了通过特定半群构造拓扑结构的方法，分析了不同半群的拓扑性质，并证明了Rubin定理，描述了Brin-Thompson群的自同构群。

Semigroup and Category-Theoretic Approaches to Partial Symmetry

This thesis is about trying to understand various aspects of partial symmetry using ideas from semigroup and category theory. In Chapter 2 it is shown that the left Rees monoids underlying self-similar group actions are precisely monoid HNN-extensions. In particular it is shown that every group HNN-extension arises from a self-similar group action. Examples of these monoids are constructed from fractals. These ideas are generalised in Chapter 3 to a correspondence between left Rees categories, self-similar groupoid actions and category HNN-extensions of groupoids, leading to a deeper relations…

On the Conjugacy Problem in Groups and its Variants

This thesis deals with the conjugacy problem in groups and its twisted variants. We analyze recent results by Bogopolski, Martino, Maslakova and Ventura on the twisted conjugacy problem in free groups and its implication for the conjugacy problem in free-by-cyclic groups and some further group extensions. We also consider the doubly-twisted conjugacy problem in free groups. Staecker has developed an algorithm for deciding doubly-twisted conjugacy relations in the case where the involved homomorphisms satisfy a certain remnant inequality. We show how a similar condition affects the equalizer su…

无限对称逆幺半群的子幺半群

Submonoids of Infinite Symmetric Inverse Monoids

本论文研究无限集上对称逆幺半群的子半群结构，通过最大子半群分类、拓扑闭子半群刻画及Bergman-Shelah预序分类三种方法，并提出了相关猜想。