Oligomorphic Groups and Their Application to the Classification of Unitary Representations
This paper explores the concept of oligomorphic groups and demonstrates how their unique properties, particularly the existence of a multiplication operation on reduced double cosets, can be utilized to classify their unitary representations.
On the Prevalence of Highly Transitive Subgroup Actions in Baumslag-Solitar Groups
This paper investigates the prevalence of highly transitive actions arising from subgroups of Baumslag-Solitar groups, revealing a strong dependence on a notion called (m,n)-phenotype, which classifies subgroups and dictates their dynamical behavior.
実質アーベル群のツイスト共役成長級数
有限生成実質アーベル群のツイスト共役成長級数は常にN-有理関数であり、群とツイスト自己準同型に関する適切な情報から明示的に計算できる。
Perfect Kernel and Dynamics of the Space of Subgroups: Exploring Applications from Bass-Serre Theory to Hyperbolic Groups
This research paper investigates the Cantor-Bendixson decomposition of the space of subgroups for various countable groups, focusing on the perfect kernel and its connection to group properties like subgroup separability, hyperbolicity, and actions on trees.
The Probability of Generating a Prosoluble Subgroup in Profinite Groups
The author conjectures that the "solubilizer" of an element in a profinite group has positive Haar measure if and only if the element centralizes almost all non-abelian chief factors of the group, and this conjecture is reduced to proving a specific property about finite simple groups.
새로운 가르사이드 구조와 아틴 군에 대한 응용
이 논문은 새로운 가르사이드 구조를 도입하여 특정 조건을 만족하는 군 G에 대해 G×Z가 가르사이드 군이 되는 방법을 제시하고, 이를 아틴 군에 적용하여 군론, 기하학, 위상수학적 결과를 도출합니다.
New Garside Structures on Direct Products of Groups with Z, with Applications to Artin Groups
This paper introduces a novel method for constructing Garside structures on the direct product of a group G and the integers (Z), under specific conditions on G. This construction yields new examples of Garside groups, including certain Artin groups, surface groups, and groups with systolic presentations, leading to new insights into their algebraic, geometric, and topological properties.
任意の残留有限性と共役分離可能性の増大度
十分に速く増大する関数はすべて、ある群の残留有限性増大関数または共役分離可能性増大関数として現れる。さらに、これらの増大関数は互いに独立しており、任意に大きく乖離する可能性がある。
On the Residual Finiteness of Groups Splitting as Finite Graphs of Free Groups with Cyclic Edge Groups
A group that can be represented as a finite graph of free groups with cyclic edge groups is residually finite if and only if it does not contain a "very unbalanced element."
グラフ積における短い正のロクソドロミック要素の構成と応用
グラフ積における正の語を用いて、一般化されたロクソドロミック要素、特に「regular」要素と「strongly irreducible」要素を効果的に生成する方法を提示し、これらの要素の存在が部分群の成長に与える影響について考察する。
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