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In the area of modern algebra known as group theory, the Conway group ''Co1'' is a sporadic simple group of order : 221395472111323 : = 4157776806543360000 : ≈ 4. ==History and properties== ''Co1'' is one of the 26 sporadic groups and was discovered by John Horton Conway in 1968. It is the largest of the three sporadic Conway groups and can be obtained as the quotient of ''Co0'' (group of automorphisms of the Leech lattice Λ that fix the origin) by its center, which consists of the scalar matrices ±1. It also appears at the top of the automorphism group of the even 26-dimensional unimodular lattice II25,1. Some rather cryptic comments in Witt's collected works suggest that he found the Leech lattice and possibly the order of its automorphism group in unpublished work in 1940. The outer automorphism group is trivial and the Schur multiplier has order 2. Co0 has no matrices of determinant -1. An inner product on the Leech lattice is defined as 1/8 the sum of the products of respective co-ordinates of the two multiplicand vectors. The norm of a vector is its inner product with itself. It is common to speak of the type of a Leech lattice vector: half the norm. This lattice has no vectors of type 1. The matrices of Co0 are orthogonal, I. e. they leave the inner product invariant. The inverse is the transpose. 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 Co1」の詳細全文を読む スポンサード リンク
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