Open AccessPresentation of the subgroups of Mathieu Group using Groupoid
Author(s) -
Nisreen Alokbi,
Faik Mayah
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1591/1/012090
Subject(s) - group (periodic table) , mathematics , presentation (obstetrics) , double groupoid , vertex (graph theory) , simple (philosophy) , pure mathematics , sporadic group , algebra over a field , combinatorics , symmetric group , alternating group , medicine , physics , graph , philosophy , epistemology , quantum mechanics , radiology
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.