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The symmetric crosscap spectrum of Abelian groups

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Abstract

Every finite group G acts on some non-orientable 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 study which natural numbers are the symmetric crosscap number of an Abelian group. This set will be called the Abelian crosscap spectrum. We obtain a full result for even numbers and describe properties satisfied by odd numbers in this spectrum.

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Authors and Affiliations

  1. Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense, 28040, Madrid, Spain

    A. Bacelo & J. J. Etayo

  2. Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, 28040, Madrid, Spain

    E. Martínez

Authors
  1. A. Bacelo
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  2. J. J. Etayo
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  3. E. Martínez
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Corresponding author

Correspondence to J. J. Etayo.

Additional information

To Professor María Teresa Lozano on occasion of her 70th birthday.

A. Bacelo and J. J. Etayo are partially supported by MTM2014-55565 and UCM910444, and E. Martínez by MTM2014-55812.

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Bacelo, A., Etayo, J.J. & Martínez, E. The symmetric crosscap spectrum of Abelian groups. RACSAM 112, 633–640 (2018). https://doi.org/10.1007/s13398-017-0434-3

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  • DOI: https://doi.org/10.1007/s13398-017-0434-3

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