Etayo Gordejuela, José JavierMartínez García, Ernesto2023-06-202023-06-202008Etayo Gordejuela, J. J. & Martínez García, E. «The Symmetric Cross-Cap Number of the Groups C m × D n ». Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 138, n.o 6, diciembre de 2008, pp. 1197-213. DOI.org (Crossref), https://doi.org/10.1017/S0308210507000169.0308-210510.1017/S0308210507000169https://hdl.handle.net/20.500.14352/50033Every 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.engjournal articlehttps//doi.org/10.1017/S0308210507000169http://journals.cambridge.org/abstract_S0308210507000169restricted access512.54Automorphism groupsKlein surfacesCross-cap numbersGrupos (Matemáticas)