Portraits of Groups on Bordered Surfaces

Jay Zimmerman
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 241–246


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.