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In mathematics, the Lyons group, Ly, is a finite sporadic simple group of order <math>2^8\cdot3^7\cdot5^6\cdot7\cdot11\cdot31\cdot37\cdot67.<math> 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 of degree 11, <math>\tilde A_{11}<math>.
It can be characterized 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.
It is named for Richard Lyons.
References
Volker Gebhardt, Two short presentations for Lyons' sporadic simple group, Experimental Mathematics, 9 (2000) no. 3, 333-338
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