Presentation of the subgroups of Mathieu Group using Groupoid

Abstract

Mathieu groups are one type of the sporadic simple groups, they turn out not to be isomorphic to any member of the infinite families of finite simple groups. Study these groups is interesting since their orders are very high. Groupoid can be used to find the presentation of the subgroups of the Mathieu groups. The idea is creating a groupoid by acting the Mathieu group on a subset of this group and then calculating the presentation of the vertex group of the groupoid which represents the presentation of the subgroup as the vertex groups are isomorphic.