Patrick Reichert

Publications

Presentation: Alternating factor groups of Fuchsian triangle groups (April 2006)

Description: This document contains the presentation slides that were used for the talk at the workshop about Belyi Maps and Dessins on Riemann Surfaces in April 2006 in Frankfurt/Main. The presentation covers the following topics:

• Existence theorems for alternating factor groups of Fuchsian triangle groups
• Search algorithms for epimorphisms into alternating groups
• Conjugacy of normal subgroups in PSL(2,R)

Keywords: Fuchsian triangle groups, alternating factor groups, conjugacy of normal subgroups in PSL(2,R)

Documents:

• Presentation slides Belyi Maps and Dessins on Riemann Surfaces in Frankfurt (April 2006)

Main results of the diploma: Alternating factor groups of Fuchsian triangle groups (January 2006)

Description: This article is the english short version of the german diploma. The german full text can also be found on this website. Only the most important chapter is contained in this paper. It is the last chapter of the original document and it was corrected on several paragraphs.

Fuchsian triangle groups have a faithful representation in PSL(2, R). This article studies the existence of epimorphisms that are mapping Fuchsian triangle groups onto alternating groups. For two different epimorphisms it is interesting whether the kernels are conjugate in PSL(2, R).

Keywords: Fuchsian triangle groups, commensurator, normalizer, torsion free subgroups

Available documents:

• Main results of the diploma (January 2006)
• Presentation slides Main results of the diploma in Magdeburg (March 2008)
• Diploma: Alternating factor groups of Fuchsian triangle groups (German, December 2003)