On Certain Small Lie Rank Subgroups of $E_8(2)$

  • Mahah Javed

Student thesis: Phd


This thesis forms a part of the much lager project whose aim is to classify the maximal subgroups of the finite simple exceptional group of Lie type $E_8(2)$. Groups $H$ with $F^*(H)$ isomorphic to $L_2(64)$, $L_2(16)$, $L_2(8)$, $L_3(4)$, or $L_3(3)$ arise as some of the possible candidates for maximal subgroups of $E_8(2)$. We prove that if $F^*(H)$ is isomorphic to $L_2(64)$, $L_2(16)$ or $L_3(4)$ then $H$ cannot be maximal in $E_8(2)$. Partial progress is made towards establishing whether $L_2(8)$ can be a maximal subgroup. A highlight is that we find maximal subgroups of $E_8(2)$ isomorphic to $L_3(3)$; we show that there are at most $3$ conjugacy classes of them. Extensive use of the computer algebra package \textsc{Magma} has been made to prove our results. After the work done in this thesis not much is left to do in order to classify the maximal subgroups of $E_8(2)$.
Date of Award1 Aug 2022
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorPeter Rowley (Supervisor) & Yuri Bazlov (Supervisor)

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