Generators and relations for the Lyons sporadic simple group

Abstract

The characterization of the sporadic simple group Ly as the universal completion of a Ly-amalgam is used to produce a new presentation for the group.

On the ranks of O’N and Ly

“…Recently, Gollan [13] proved the existence and uniqueness of Ly independently using the two permutations provided by Cooperman et al in [9], while Parker in [25] obtained a new presentation using the Ly-amalgam. The group Ly has 11 conjugacy classes of maximal subgroups as determined by Wilson [29] and listed in the ATLAS.…”

“…For more information about the group Ly, the reader is referred to [14,19,25,26]. Next we compute the rank for each conjugacy class nX of Ly.…”

Heuristics for cannon's algorithm with an application to lyons sporadic group

“…This group is a sporadic simple group whose existence was predicted by Lyons [3] in 1972. Using the group properties, C. Parker [4] gave a presentation with 17 variables and 51 relations. By a computational approach, V. Gebhardt [2] used his Double Coset Cannon Algorithm to produce a presentation with 5 variables and 25 relations for a global length is equal to 549.…”