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Triangle Groups as Subgroups of Unitary Groups

✍ Scribed by Maxim Vsemirnov; Vitaliy Mysovskikh; M.Chiara Tamburini

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 177 KB
Volume: 245
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8945

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✦ Synopsis

This paper presents a new approach to 2 3 k -generated groups. We first show that the triangle group T 2 3 k is isomorphic to a subgroup of a two-dimensional projective unitary group over a ring. Then our main purpose is to determine the values of k for which this subgroup coincides with the whole projective unitary group. We answer this question in full generality, showing that equality holds precisely when k ∈ 2 3 4 5 7 9 11 . The methods come from algebraic number theory.

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