Factorisations of sporadic simple groups

On Minimal Factorisations of Sporadic Groups

For many years cryptographers have used large abelian finite groups but some are now turning their attention to non-abelian ones. They feel that these could be a good source of “trap doors” that can be used in public key encryption [Magliveras 02]. One proposed system is MST1 [Magliveras 02]. This uses a certain type of group factorisation to encode messages which can only be decoded by the rec...

Unitriangular factorisations of Chevalley groups

Semi-Presentations for the Sporadic Simple Groups

A semi-presentation for a group G is a set of relations which characterises a set of generators of G up to automorphism. We discuss some techniques for finding semi-presentations and illustrate them by exhibiting semi-presentations on standard generators for the 26 sporadic simple groups and their automorphism groups. We then show how these semipresentations were used to check the data in the W...

Base sizes for sporadic simple groups

Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. We write b(G) for the minimal size of a base for G. We determine the precise value of b(G) for every primitive almost simple sporadic group G, with the exception of two cases involving the Baby Monster group. As a corollary, we deduce that b(G) 6 7, with equality if and onl...

Local Fusion Graphs and Sporadic Simple Groups

For a group G with G-conjugacy class of involutions X, the local fusion graph F(G,X) has X as its vertex set, with distinct vertices x and y joined by an edge if, and only if, the product xy has odd order. Here we show that, with only three possible exceptions, for all pairs (G,X) with G a sporadic simple group or the automorphism group of a sporadic simple group, F(G,X) has diameter 2.