Algorithms determining finite simple images of finitely presented groups
Algorithms determining finite simple images of finitely presented groups
复制标题
确定有限呈现群的有限简单图像的算法
作者：
M. Bridson;D. Evans;M. Liebeck;D. Segal
我们解决了这样一个问题：对于哪些有限简单群的集合，存在一种算法来确定集合中任意有限呈现群的图像？我们证明了积极和消极的结果。对于包含无穷多个交替群或包含无界维经典群的有限简单群的集合，我们证明了不存在这样的算法。另一方面，对于有界秩的Lie型单群族，我们得到了积极的结果。例如，对于任何固定的未扭曲Lie类型X，存在一种算法，该算法确定给定的有限呈现群对于无穷多个q是否具有形式为X(q)的简单图像，如果有有限多个，则该算法确定它们。
We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups, or contains classical groups of unbounded dimensions, we prove that there is no such algorithm. On the other hand, for families of simple groups of Lie type of bounded rank, we obtain positive results. For example, for any fixed untwisted Lie type X there is an algorithm that determines whether or not any given finitely presented group has simple images of the form X(q) for infinitely many q, and if there are finitely many, the algorithm determines them.
影响因子：
3.1
作者：
Bridson M
通讯作者：
Bridson M
影响因子：
1.8
作者：
Liebeck, Martin W.;Macpherson, Dugald;Tent, Katrin
通讯作者：
Tent, Katrin