Lyons group
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In the mathematical field of group theory, the Lyons group Ly (named after Richard Lyons), is a finite group of order
- 28 · 37 · 56 · 7 · 11 · 31 · 37 · 67
- = 51765179004000000
- ≈ 5 · 10 16 .
It is a simple group, meaning it does not have any normal subgroups except for the subgroup consisting only of the identity element, and Ly itself.
The Lyons group is one of the 26 sporadic groups. It can be characterized as the unique simple group where the centralizer of an involution, and hence of all the involutions, is isomorphic to the nontrivial central extension of the cyclic group C2 by the alternating group A11 of degree 11.
It can be described more concretely in terms of a modular representation of dimension 111 over the field of five elements, or in terms of generators and relations, for instance those given by Gebhardt.
[edit] References
Volker Gebhardt, Two short presentations for Lyons' sporadic simple group, Experimental Mathematics, 9 (2000) no. 3, 333-338.
