群作用、变形、多群扩张和群表示
Group actions, deformations, polygroup extensions, and group presentations
摘要：
推广经典扩张理论，我们解决了一个Schreier型扩张问题的多群群。因此，我们得到了一个方法来计算一个组的介绍，从它的行动在一个集合。该方法的有用性是通过推导出明确的介绍为集团$GL_2$在赋值环和超过价值的领域，集团$SL_3$在任意领域，以及为五个马蒂厄集团。此外，我们勾勒出一些方面的一个新的变形技术的群体，他们的行动，并介绍，并将其应用到计算介绍的急剧$3$ -传递Zassenhaus群$M(q^2)$（在符号的Huppert和Blackburn）的任何奇素数权力$q$。这种计算用于演示如何适当的变形的群体和他们的行动相互作用，从而提高，演示方法。
英文摘要：
Generalizing classical extension theory, we solve a Schreier-type extension problem for polygroups by groups. As a consequence, we obtain a method for computing a presentation for a group from its action on a set. The usefulness of this method is illustrated by deriving explicit presentations for the groups $GL_2$ over valuation rings and over valued fields, for the groups $SL_3$ over arbitrary fields, as well as for the five Mathieu groups. Moreover, we sketch some aspects of a new deformation technique for groups, their actions, and presentations, and apply it to compute presentations for the sharply $3$-transitive Zassenhaus groups $M(q^2)$ (in the notation of Huppert and Blackburn) for any odd prime power $q$. This computation serves to demonstrate how suitable deformation of groups and their actions interacts with, and thereby enhances, the presentation method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
