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Higman group : ウィキペディア英語版
Higman group

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
:a^ba=b^2,\quad b^cb=c^2,\quad c^dc=d^2,\quad d^ad=a^2.
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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