|
In the area of modern algebra known as group theory, the monster group ''M'' (also known as the Fischer–Griess monster, or the Friendly Giant) is a sporadic simple group of order : 2463205976112133171923293141475971 : = 808017424794512875886459904961710757005754368000000000 : = 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 : ≈ 8. The finite simple groups have been completely classified. Every such group belongs to one of 18 countably infinite families, plus 26 sporadic groups that do not follow such a systematic pattern. The monster group is the largest of these sporadic groups and contains all but six of the other sporadic groups as subquotients. Robert Griess has called these 6 exceptions pariahs, and refers to the other 20 as the ''happy family''. ==History== The monster was predicted by Bernd Fischer (unpublished) and in about 1973 as a simple group containing a double cover of Fischer's Baby Monster group as a centralizer of an involution. Within a few months the order of M was found by Griess using the Thompson order formula, and Fischer, Conway, Norton and Thompson discovered other groups as subquotients, including many of the known sporadic groups, and two new ones: the Thompson group and the Harada–Norton group. constructed M as the automorphism group of the Griess algebra, a 196,884-dimensional commutative nonassociative algebra. and subsequently simplified this construction. Griess's construction showed that the monster existed. showed that its uniqueness (as a simple group satisfying certain conditions coming from the classification of finite simple groups) would follow from the existence of a 196,883-dimensional faithful representation. A proof of the existence of such a representation was announced by , though he has never published the details. gave the first complete published proof of the uniqueness of the monster (more precisely, they showed that a group with the same centralizers of involutions as the monster is isomorphic to the monster). The Schur multiplier and the outer automorphism group of the monster are both trivial. 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「monster group」の詳細全文を読む スポンサード リンク
|