%0 Journal Article
%A Etayo Gordejuela, José Javier
%A Martínez García, Ernesto
%T The symmetric crosscap number of the groups Cm × Dn
%D 2008
%@ 0308-2105
%U https://hdl.handle.net/20.500.14352/50033
%X 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 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.
%~