论文标题
最终几乎没有免费组的内态固定点
Eventually fixed points of endomorphisms of virtually free groups
论文作者
论文摘要
我们通过几乎没有自由组的内态性的作用来考虑有限轨道点的点子组，并特别强调了最终固定点的子组，即evfix（$φ$）：轨道包含固定点的点。我们提供了一种算法来计算有限生成的实际生成的固定点的子组的子组，并证明有限的轨道具有可计算常数为界限的基数，这使我们可以解决几个算法问题：确定$φ$是否是$ g $的有限量（如果$ g $），如果$ $ $φ生成的，在免费组中，EVFIX（$φ$）是否是$ f_n $的普通亚组。如果有限地生成，我们还为EVFIX（$φ$）的等级提供了一个界限。
We consider the subgroup of points of finite orbit through the action of an endomorphism of a virtually free group, with particular emphasis on the subgroup of eventually fixed points, EvFix($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.
