The symmetric crosscap spectrum of Abelian groups
| Autor: | Adrián Bacelo, J. J. Etayo, E. Martínez |
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| Rok vydání: | 2017 |
| Předmět: |
Finite group
Algebra and Number Theory Group (mathematics) Applied Mathematics 010102 general mathematics Natural number Computer Science::Computational Geometry Mathematics::Geometric Topology 01 natural sciences Spectrum (topology) Combinatorics 03 medical and health sciences Computational Mathematics 0302 clinical medicine Genus (mathematics) 030212 general & internal medicine Geometry and Topology 0101 mathematics Abelian group Crosscap number Analysis Mathematics |
| Zdroj: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 112:633-640 |
| ISSN: | 1579-1505 1578-7303 |
| DOI: | 10.1007/s13398-017-0434-3 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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