Torsion in maximal arithmetic Fuchsian groups

Colin MacLachlan

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper, formulas are derived for the number of conjugacy classes of finite cyclic subgroups in a family of arithmetic Fuchsian groups which includes all maximal arithmetic Fuchsian groups. These formulas are given in terms of the arithmetic data which defines the group. Since a formula for the co-area of these groups in similar terms is also known, this means that the signature and hence isomorphism class of any maximal arithmetic Fuchsian group can be completely determined from the arithmetic data defining the group.
Original languageEnglish
Title of host publicationCombinatorial Group Theory, Discrete Groups, and Number Theory
Place of PublicationProvidence, RI, USA
PublisherAmerican Mathematical Society
Pages213-225
Number of pages13
Volume421
ISBN (Print)0821839853, 978-0821839850
Publication statusPublished - 18 Jan 2007
EventASM Special Meeting on Infinite Group Theory - New York, United States
Duration: 8 Oct 20059 Oct 2005

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
Volume421
ISSN (Print)0271-4132

Conference

ConferenceASM Special Meeting on Infinite Group Theory
CountryUnited States
CityNew York
Period8/10/059/10/05

Fingerprint

Arithmetic Groups
Fuchsian Group
Torsion
Isomorphism Classes
Conjugacy class
Signature
Subgroup
Term

Cite this

MacLachlan, C. (2007). Torsion in maximal arithmetic Fuchsian groups. In Combinatorial Group Theory, Discrete Groups, and Number Theory (Vol. 421, pp. 213-225). (Contemporary Mathematics; Vol. 421). Providence, RI, USA: American Mathematical Society.

Torsion in maximal arithmetic Fuchsian groups. / MacLachlan, Colin.

Combinatorial Group Theory, Discrete Groups, and Number Theory. Vol. 421 Providence, RI, USA : American Mathematical Society, 2007. p. 213-225 (Contemporary Mathematics; Vol. 421).

Research output: Chapter in Book/Report/Conference proceedingChapter

MacLachlan, C 2007, Torsion in maximal arithmetic Fuchsian groups. in Combinatorial Group Theory, Discrete Groups, and Number Theory. vol. 421, Contemporary Mathematics, vol. 421, American Mathematical Society, Providence, RI, USA, pp. 213-225, ASM Special Meeting on Infinite Group Theory , New York, United States, 8/10/05.
MacLachlan C. Torsion in maximal arithmetic Fuchsian groups. In Combinatorial Group Theory, Discrete Groups, and Number Theory. Vol. 421. Providence, RI, USA: American Mathematical Society. 2007. p. 213-225. (Contemporary Mathematics).
MacLachlan, Colin. / Torsion in maximal arithmetic Fuchsian groups. Combinatorial Group Theory, Discrete Groups, and Number Theory. Vol. 421 Providence, RI, USA : American Mathematical Society, 2007. pp. 213-225 (Contemporary Mathematics).
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