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In mathematics, the Higman group, introduced by , was the first example of an infinite finitely presented group with no non-trivial finite quotients. The quotient by the maximal proper normal subgroup is a finitely generated infinite simple group. later found some finitely presented infinite groups ''G''''n'',''r'' that are simple if ''n'' is even and have a simple subgroup of index 2 if ''n'' is odd, one of which is one of the Thompson groups. Higman's group is generated by 4 elements ''a'', ''b'', ''c'', ''d'' with the relations :. ==References== * * 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「Higman group」の詳細全文を読む スポンサード リンク
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