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

Published online by Cambridge University Press:  23 December 2016

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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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