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In mathematics, a group of Lie type is a group closely related to the group, ''G''(''k''), of rational points of a reductive linear algebraic group, ''G'', with values in the field, ''k''. Finite groups of Lie type give the bulk of non-abelian finite simple groups. Special cases include the classical groups, the Chevalley groups, the Steinberg groups, and the Suzuki–Ree groups. All Lie groups are groups of Lie type, but not vice-versa. and are standard references for groups of Lie type. ==Classical groups== (詳細はfields by . These groups were studied by L. E. Dickson and Jean Dieudonné. Emil Artin investigated the orders of such groups, with a view to classifying cases of coincidence. A classical group is, roughly speaking, a special linear, orthogonal, symplectic, or unitary group. There are several minor variations of these, given by taking derived subgroups or central quotients, the latter yielding projective linear groups. They can be constructed over finite fields (or any other field) in much the same way that they are constructed over the real numbers. They correspond to the series A''n'', B''n'', C''n'', D''n'',2A''n'', 2D''n'' of Chevalley and Steinberg groups. 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「Group of Lie type」の詳細全文を読む スポンサード リンク
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