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Etayo Gordejuela, J. Javier and Martínez García, Ernesto
(2008)
*The symmetric crosscap number of the groups Cm × Dn.*
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 138
(6).
pp. 1197-1213.
ISSN 0308-2105

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Official URL: http://journals.cambridge.org/abstract_S0308210507000169

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http://www.cambridge.org/ | Publisher |

## Abstract

Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric cross-cap number and denoted by ˜σ(G). This number is related to other parameters defined on surfaces as the symmetric genus and the strong symmetric genus. The systematic study of the symmetric cross-cap number was begun by C. L. May, who also calculated it for certain finite groups. Here we obtain the symmetric cross-cap number for the groups Cm ×Dn. As an application of this result, we obtain arithmetic sequences of integers which are the symmetric cross-cap number of some group. Finally, we recall the several different genera of the groups Cm × Dn.

Item Type: | Article |
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Uncontrolled Keywords: | Automorphism groups; Klein surfaces; cross-cap numbers |

Subjects: | Sciences > Mathematics > Group Theory |

ID Code: | 15812 |

Deposited On: | 03 Jul 2012 09:03 |

Last Modified: | 19 Feb 2019 09:44 |

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