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2016-12-27T19:40:53Z

‎Bibtex

Gubachelier: Die Seite wurde neu angelegt: „ == Reference == Jay Zimmerman: Portraits of Groups on Bordered Surfaces. In: Bridges 2016, Pages 241–246. == DOI == == Abstract == This paper lo…“

2016-12-26T22:43:24Z

Die Seite wurde neu angelegt: „ == Reference == Jay Zimmerman: Portraits of Groups on Bordered Surfaces. In: Bridges 2016, Pages 241–246. == DOI == == Abstract == This paper lo…“

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== Reference ==
Jay Zimmerman: [[Portraits of Groups on Bordered Surfaces]]. In: [[Bridges 2016]], Pages 241–246.

== DOI ==

== Abstract ==
This paper looks at representing a group G as a group of transformations of an orientable compact bordered Klein surface. We construct visual representations (portraits) of three groups S4, Z2  S3 and a group L* of order 32. These groups have real genus 3, 2 and 5 respectively. The first two groups are M*-groups; which means that they act on surfaces with maximal symmetry. They are also the only solvable M* - simple groups.

== Extended Abstract ==

== Bibtex ==
@inproceedings{bridges2016:241,
author = {Jay Zimmerman},
title = {Portraits of Groups on Bordered Surfaces},
pages = {241--246},
booktitle = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
year = {2016},
editor = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
isbn = {978-1-938664-19-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
url = {http://de.evo-art.org/index.php?title=Portraits_of_Groups_on_Bordered_Surfaces},
note = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-241.html}}
}

== Used References ==
1. W. Burnside, Theory of groups of finite order, (Cambridge University Press 1911).

2. E. Bujalance, J.J. Etayo, J.M. Gamboa and G. Gromadzki, Automorphism Groups of Compact Bordered Klein Surfaces, A Combinatorial Approach, Lecture Notes in Mathematics 1439, Springer-Verlag, Berlin, Heidelberg, 1990.

3. Coxeter, H.S.M. and Moser, W.O.J., Generators and Relations for Discrete Group, Reprint of Fourth Ed., Springer-Verlag, New York 1984.

4. N. Greenleaf and C. L. May, Bordered Klein surfaces with maximal symmetry, Trans. Amer. Math. Soc. 274 (1982), 265 – 283.

5. C. L. May, Groups of small real genus, Houston J. Math. 20, No. 3, (1994), 393 – 408.

6. J. J. van Wijk, Symmetric Tilings of Closed Surfaces: Visualization of Regular Maps, ACM Transactions on Graphics, vol. 28, no. 3, Article 49 (2009) Proceedings ACM SIGGRAPH’09.

7. J. Zimmerman, Portraits of Groups, Conference Proceedings 2006, Bridges London: Mathematical Connections in Art, Music and Science, London, England, 131 - 134.

8. J. Zimmerman, A Portrait of a Quadrilateral Group, Conference Proceedings 2011, Bridges Coimbra: Mathematical Connections in Art, Music and Science, Coimbra, Portugal, 505 - 508.

== Links ==
=== Full Text ===
http://archive.bridgesmathart.org/2016/bridges2016-241.pdf

[[intern file]]

=== Sonstige Links ===
http://archive.bridgesmathart.org/2016/bridges2016-241.html

@@ Zeile 23: / Zeile 23: @@
    publisher   = {Tessellations Publishing},
    address     = {Phoenix, Arizona},
-   url         = {http://de.evo-art.org/index.php?title=Portraits_of_Groups_on_Bordered_Surfaces},
+   url         = {http://de.evo-art.org/index.php?title=Portraits_of_Groups_on_Bordered_Surfaces },
    note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-241.html}}
+  }
 == Used References ==

Portraits of Groups on Bordered Surfaces - Versionsgeschichte

Gubachelier: /* Bibtex */

Gubachelier: Die Seite wurde neu angelegt: „ == Reference == Jay Zimmerman: Portraits of Groups on Bordered Surfaces. In: Bridges 2016, Pages 241–246. == DOI == == Abstract == This paper lo…“