有界型的近全群，第2部分
Near full groups of bounded type, II
浏览论文内容
中文总结 AI 辅助
本研究给出有界型群包含AF交错群的充分条件，通过相关概念对公度过程公理化，分离出产生选择器的碎裂，还证明改进的Fabrykowski-Gupta群的碎裂群满足特定性质。
中文摘要 AI 辅助
我们给出有界型群包含AF交错群的充分条件，通过交错数据、对角继承、选择器传播和有界吸收对公度过程进行公理化，还分离出一类能产生选择器的碎裂。作为应用，我们证明改进的Fabrykowski-Gupta群的碎裂群包含AF交错群，吸收延迟至多为2，且其奇偶完备等于它的拓扑全群。
英文摘要
Containment of the AF alternating group of the tail groupoid is the AF input in our full-group completion theorem for groups satisfying the finite singular germ condition. We give a sufficient criterion for this containment, in which selectors separate inherited diagonal actions, and an exact criterion for finite regular coverings. We then identify a class of fragmentations that produce the required selectors. In the covering case, the intersection with the AF alternating group is the centralizer of the subgroup of deck transformations commuting with the adjoined AF permutations. This yields finitely generated examples with minimal actions and identical groupoids of germs but different intersections with the AF alternating group. Consequently, containment of the AF alternating group is not determined by the groupoid of germs alone. As an application, we show that a fragmentation group of the modified Fabrykowski--Gupta group contains the AF alternating group and, by the completion theorem, has index four in its topological full group.
发表机构
- School of Mathematics, South China University of Technology（华南理工大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。
