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The Automorphism Groups on the Complex Plane
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The automorphism groups in the complex plane are defined, and we prove that they satisfy the group axioms. The automorphism group is derived for some domains. By applying the Riemann mapping theorem, it is proved that every automorphism group on simply connected domains that are proper subsets of the complex plane, is isomorphic to the automorphism group on the unit disc.

Abstract [sv]

Automorfigrupperna i det komplexa talplanet definieras och vi bevisar att de uppfyller gruppaxiomen. Automorfigruppen på några domän härleds. Genom att applicera Riemanns avbildningssats bevisas att varje automorfigrupp på enkelt sammanhängande, öppna och äkta delmängder av det komplexa talplanet är isomorf med automorfigruppen på enhetsdisken.

Place, publisher, year, edition, pages
2017.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:umu:diva-139446OAI: oai:DiVA.org:umu-139446DiVA: diva2:1140712
Supervisors
Examiners
Available from: 2017-10-30 Created: 2017-09-13 Last updated: 2017-10-30Bibliographically approved

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Mathematical Analysis

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  • apa
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  • de-DE
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