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Etayo Gordejuela, J. Javier and Gromadzki, G. and Martínez García, Ernesto
(2012)
*The symmetric crosscap number of the families of groups DC3 × Cn and A4 × Cn.*
Houston Journal of Mathematics, 38
(2).
pp. 345-358.
ISSN 0362-1588

Official URL: http://math.uh.edu/~hjm/restricted/pdf38(2)/02gordejuela.pdf

## 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 crosscap number and denoted by σ˜(G). The systematic study about the symmetric crosscap number was begun by C. L. May who also calculated it for certain finite groups. It is known that 3 cannot be the symmetric crosscap number of a group. Conversely, all integers non-congruent with 3 or 7 modulo 12 are the symmetric crosscap number of some group. Here we obtain the symmetric crosscap number for the families of groups DC3× Cn and A4× Cn and we prove that their values cover a quarter of the numbers congruent with 3 modulo 12 and three quarters of the numbers congruent with 7 modulo 12. As a consequence there are only five integers lower than 100 which are not known if they are the symmetric crosscap number of some group.

Item Type: | Article |
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Uncontrolled Keywords: | Klein surfaces; automorphism |

Subjects: | Sciences > Mathematics > Group Theory |

ID Code: | 15816 |

Deposited On: | 03 Jul 2012 10:13 |

Last Modified: | 03 Jul 2012 10:13 |

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