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SYMMETRIC CROSSCAP NUMBER OF GROUPS OF ORDER LESS THAN OR EQUAL TO 63

Part of: Low-dimensional topology Special aspects of infinite or finite groups Riemann surfaces Other groups of matrices

Published online by Cambridge University Press:  23 December 2016

ADRIÁN BACELO Open the ORCID record for ADRIÁN BACELO [Opens in a new window]
ADRIÁN BACELO*
Affiliation:
Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain email [email protected]
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Abstract

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Every finite group $G$ acts on some nonorientable unbordered surfaces. The minimal topological genus of those surfaces is called the symmetric crosscap number of $G$. It is known that 3 is not the symmetric crosscap number of any group but it remains unknown whether there are other such values, called gaps. In this paper we obtain group presentations which allow one to find the actions realizing the symmetric crosscap number of groups of each group of order less than or equal to 63.

Keywords

Riemann surfacesGroup theoryKlein surfaces

MSC classification

Primary: 57M60: Group actions in low dimensions
Secondary: 20F05: Generators, relations, and presentations 20H10: Fuchsian groups and their generalizations 30F50: Klein surfaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 103 , Issue 2 , October 2017 , pp. 145 - 156
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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