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Título:
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The symmetric crosscap number of the families of groups DC3 × Cn and A4 × Cn
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Autores:
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Etayo Gordejuela, J. Javier ;
Gromadzki, G. ;
Martínez García, Ernesto
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Tipo de documento:
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texto impreso
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Editorial:
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University of Houston, 2012
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Grupos (Matemáticas)
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Tipo = Artículo
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Resumen:
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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 ?˜(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.
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