几乎自由群组内定点的最终定点

IF 0.6 4区 数学 Q3 MATHEMATICS
André Carvalho
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引用次数: 0

摘要

我们考虑通过有限生成的无形似群的内态化作用的有限轨道点的子群,特别强调最终固定点的子群,$text{EvFix}(\varphi)$:轨道包含一个固定点的点。我们提供了一种算法来计算有限生成的 virtually free 群的内定点子群,并证明了有限轨道的心性受一个可计算常数的约束,这使我们能够解决几个算法问题:决定φ是否是$\text{End}(G)$的有限阶元素,φ是否是非周期性的,$\text{EvFix}(\varphi)$是否是有限生成的,以及$\text{EvFix}(\varphi)$是否是一个正常子群。在$\text{EvFix}(\varphi)$是有限生成的情况下,我们还给出了它的秩的约束和计算生成集的算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Eventually fixed points of endomorphisms of virtually free groups
We consider the subgroup of points of finite orbit through the action of an endomorphism of a finitely generated virtually free group, with particular emphasis on the subgroup of eventually fixed points, $\text{EvFix}(\varphi)$: points whose orbit contains a fixed point. We provide an algorithm to compute the subgroup of fixed points of an endomorphism of a finitely generated virtually free group and prove that finite orbits have cardinality bounded by a computable constant, which allows us to solve several algorithmic problems: deciding if φ is a finite order element of $\text{End}(G)$, if φ is aperiodic, if $\text{EvFix}(\varphi)$ is finitely generated and if $\text{EvFix}(\varphi)$ is a normal subgroup. In the cases where $\text{EvFix}(\varphi)$ is finitely generated, we also present a bound for its rank and an algorithm to compute a generating set.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
36
审稿时长
6-12 weeks
期刊介绍: The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.
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