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In the area of modern algebra known as group theory, the Harada–Norton group ''HN'' is a sporadic simple group of order : 214365671119 : = 273030912000000 : ≈ 3. ==History and properties== ''HN'' is one of the 26 sporadic groups and was found by and ). Its Schur multiplier is trivial and its outer automorphism group has order 2. ''HN'' has an involution whose centralizer is of the form 2.HS.2, where HS is the Higman-Sims group (which is how Harada found it). The prime 5 plays a special role in the group. For example, it centralizes an element of order 5 in the Monster group (which is how Norton found it), and as a result acts naturally on a vertex operator algebra over the field with 5 elements . This implies that it acts on a 133 dimensional algebra over F5 with a commutative but nonassociative product, analogous to the Griess algebra . 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「Harada–Norton group」の詳細全文を読む スポンサード リンク
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