A presentation for the Thompson sporadic simple group (Q2759628)

Sporadic groups are in a certain sense the most fascinating among the finite simple groups. Hence for a lot of them even different presentations by generators and relations are known. Which one prefers is sometimes a matter of taste. It is a remarkable fact that no such presentation for Thompson's simple group \(Th\) was known. The purpose of this paper is to close this gap. The authors give a very nice presentation for the group, which has the advantage that one can see the relevant subgroups of \(Th\) as there are \(^3D_4(2)\), \(^3D_4(2):3\), \(G_2(3): 2\), \(2^{1+8}A_9\) (the involution centralizer) and \(2^5L_5(2)\) (the Dempwolff group). The generators and relations where motivated and found by investigating the 248-dimensional representation over \(\text{GF}(2)\) (matrices can be found in \texttt{www.mat.bham.ac.uk/atlas/gap/Th/}). Then they use coset enumeration on a supercomputer over the subgroup \(3D_4(2):3\) which is of index 143127000.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00030].