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In mathematics, especially group theory, the Zappa–Szép product (also known as the Zappa–Rédei-Szép product, general product, knit product or exact factorization) describes a way in which a group can be constructed from two subgroups. It is a generalization of the direct and semidirect products. It is named after Guido Zappa (1940) and Jenő Szép (1950) although it was independently studied by others including B.H. Neumann (1935), G.A. Miller (1935), and J.A. de Séguier (1904). ==Internal Zappa–Szép products== Let ''G'' be a group with identity element ''e'', and let ''H'' and ''K'' be subgroups of ''G''. The following statements are equivalent: * ''G'' = ''HK'' and ''H'' ∩ ''K'' = * For each ''g'' in ''G'', there exists a unique ''h'' in ''H'' and a unique ''k'' in ''K'' such that ''g = hk''. If either (and hence both) of these statements hold, then ''G'' is said to be an internal Zappa–Szép product of ''H'' and ''K''. 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「Zappa–Szép product」の詳細全文を読む スポンサード リンク
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