Words for Maximal Subgroups in Certain Sporadic Simple Groups

Abstract

In this thesis we found generators for the Maximal Subgroups (MSs) of the Sporadic Simple Groups (SSGs) as words in the generators of the parent group. The idea of standard generators was presented by Wilson. He began a project known as online form of Atlas, ”http://brauer.maths.qmul.ac.uk/Atlas” in which he provides the representation and words for MSs of the SSGs. However there are some cases, which have to be dealed. We pursue the work initiated by R. A. Wilson of finding words for the MSs of SSG. Thus the only cases on the list of World-wide-web Atlas which need to be solved are Co1, HN, Fi23, Fi0 24, B and M. There are 14 MSs of Harada-Norton group HN. Generators of 11 MSs are already known. In this thesis we have provided generators of remaining 3 MSs. Similarly, we have provided words for four MSs of Fi23, words for sixteen MSs of Co1, words for 11 MSs of Fi0 24 and words for MSs of some linear groups. In World-Wide-Web Atlas of group representation there is only one copy of S5 of the MSs of L3(5), but we have found words for two non-conjugate copies of S5 in Table 15 of second chapter.