Group actions, deformations, polygroup extensions, and group   presentations
  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. 
Serban A. Basarab (Romanian Academy) and Thomas W. M\"uller (Queen   Mary and Westfield College, University of London)
math.GR