有界类型的近全群，其一
Near full groups of bounded type: full group completion
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中文总结 AI 辅助
研究有界类型群的子类，由布拉特雷图平铺膨胀产生的有限生成群，在自然局部化假设下添加有限变换可得拓扑全群，在额外假设下原群在拓扑全群中有有限指数甚至重合。
中文摘要 AI 辅助
我们描述了有界类型群的一个子类，它们与其拓扑全群相差不远，即它们在拓扑全群中有有限指数。更确切地说，我们研究了由布拉特雷图上的平铺膨胀产生的有限生成群，这些群包含布拉特雷图尾群胚的AF交错群。在自然局部化假设下，添加有限多个有限变换可得到整个拓扑全群。在额外假设下，原群在拓扑全群中有有限指数，且在某些情况下与之重合。
英文摘要
We study finitely generated groups of bounded type arising from tile inflation processes over Bratteli diagrams and containing the alternating group of the associated tail groupoid. Under a localization condition on finitely many singular germs, we show that the topological full group is obtained by adjoining finitely many finitary transformations. The number of adjoined transformations can be taken to be the dimension of a quotient of the mod-$2$ dimension group, and equality with the topological full group is characterized by surjectivity of the parity map restricted to the finitary elements of the original group. Under an additional parity condition on the AF truncations arising in the localization, the original group is near full, and its index is the order of the same parity quotient. We give a criterion for localization in terms of finitely many representatives of singular germs preserving arbitrarily deep cylinders, and an odd-order criterion which implies the parity condition. As an application, we study a fragmentation group of the modified LMS-group associated with the Penrose tiling and prove that it coincides with its topological full group.
