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In the area of modern algebra known as group theory, the Conway groups are the three sporadic simple groups ''Co1'', ''Co2'' and ''Co3'' along with the related but non-sporadic finite group ''Co0'' introduced by . The largest of the Conway groups, Co0, is the group of automorphisms of the Leech lattice Λ. It has order : 8,315,553,613,086,720,000 but it is not a simple group. The group Co1 has order : 4,157,776,806,543,360,000 and it is obtained as the quotient of Co0 by its center, which consists of the scalar matrices ±1. The groups Co2 (of order 42,305,421,312,000) and Co3 (of order 495,766,656,000) consist of the automorphisms of Λ fixing a lattice vector of type 2 and a vector of type 3 respectively. (The type of a vector is half of its square norm, ''v·v''.) As the scalar −1 fixes no non-zero vector, these two groups are isomorphic to subgroups of Co1. ==History== relates how John Leech about 1964 investigated close packings of spheres in Euclidean spaces of large dimension. One of Leech's discoveries was a lattice packing in 24-space, based on what came to be called the Leech lattice Λ. He wondered whether his lattice's symmetry group contained an interesting simple group, but felt he needed the help of someone better acquainted with group theory. He had to do much asking around because the mathematicians were pre-occupied with agendas of their own. John Conway agreed to look at the problem. John G. Thompson said he would be interested if he were given the order of the group. Conway expected to spend months or years on the problem, but found results in just a few sessions. stated that he found the Leech lattice in 1940 and hinted that he calculated the order of its automorphism group (the double cover of Conway's largest simple group). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Conway group」の詳細全文を読む スポンサード リンク
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