Osaka Journal of Mathematics

Jø rgensen subgroups of the Picard group

Francisco González-Acuña and Arturo Ramírez

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Abstract

Let $G$ be a subgroup of rank two of the Möbius group $\textit{PSL}(2, \mathbb{C})$. The Jørgensen number $J(G)$ of $G$ is defined by \[ J(G) = \inf \{|\tr^{2} A - 4| + \mathopen|\tr[A, B]-2|\colon \langle A, B\rangle= G\}. \] We describ e all subgroups $G$ of the Picard group $\textit{PSL}(2, \mathbb{Z} + i\mathbb{Z})$ with $J(G) = 1$.

Article information

Source
Osaka J. Math., Volume 44, Number 2 (2007), 471-482.

Dates
First available in Project Euclid: 5 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1183667991

Mathematical Reviews number (MathSciNet)
MR2351012

Zentralblatt MATH identifier
1142.30016

Subjects
Primary: 30F40: Kleinian groups [See also 20H10]
Secondary: 20E06: Free products, free products with amalgamation, Higman-Neumann- Neumann extensions, and generalizations

Citation

González-Acuña, Francisco; Ramírez, Arturo. Jø rgensen subgroups of the Picard group. Osaka J. Math. 44 (2007), no. 2, 471--482. https://projecteuclid.org/euclid.ojm/1183667991


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