Group generated by half transvections

• Tsuboi Takashi

  GRADUATE SCHOOL OF MATHEMATICAL SCIENCES UNIVERSITY OF TOKYO

抄録

Consider the group SL(2; Z) acting on the circle consisting of rays from the origin in R². The action of parabolic elements or transvections X∈SL(2; Z) (Tr X=2) have 2 fixed points on the circle. A half transvection is the restriction of the action of a parabolic element to one of the invariant arcs extended by the identity on the other arc. We show that the group G generated by half transvections is isomorphic to the Higman-Thompson group T, which is a finitely presented infinite simple group. A finite presentation of the group T has been known, however, we explain the geometric way to obtain a finite presentation of the group T by the Bass-Serre-Haefliger theory. We also give a finite presentation of the group T by the generators which are half transvections.

収録刊行物

• ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ

  ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ 28 (3), 463-482, 2005

  国立大学法人 東京工業大学理学院数学系

キーワード

• General Mathematics

詳細情報

• CRID: 1390001205271618560
• NII論文ID: 130003574505
• DOI: 10.2996/kmj/1134397761
• ISSN: 18815472
• ISSN: 03865991
• MRID: 2194538
• 本文言語コード: en
• データソース種別:
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