虚自由群自同态的最终不动点
Eventually fixed points of endomorphisms of virtually free groups
摘要：
我们考虑有限轨道的点的子群通过一个自同态的作用的一个虚拟的自由群，特别强调子群的最终不动点，EvFix（$φ$）：点的轨道包含一个不动点。我们提供了一个算法来计算一个随机生成的虚拟自由群的自同态的不动点的子群，并证明了有限轨道具有由一个可计算常数限定的基数，这允许我们解决几个算法问题：判断$φ$是否是End的有穷级元素（$G$），如果$φ$是非周期性的，如果EvFix（$φ$）是随机生成的，以及在自由群的情况下，EvFix（$φ$）是否是$F_n$的正规子群。我们还提出了一个边界的EvFix（$φ$）的秩的情况下，它是随机生成的。
英文摘要：
We consider the subgroup of points of finite orbit through the action of an endomorphism of a virtually free group, with particular emphasis on the subgroup of eventually fixed points, EvFix($φ$): 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 End($G$), if $φ$ is aperiodic, if EvFix($φ$) is finitely generated and, in the free group case, whether EvFix($φ$) is a normal subgroup of $F_n$ or not. We also present a bound for the rank of EvFix($φ$) in case it is finitely generated.
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