%0 Journal Article
%A Etayo Gordejuela, J. Javier
%A Gromadzki, G.
%A Martínez García, Ernesto
%T The symmetric crosscap number of the families of groups DC3 × Cn  and A4 × Cn
%D 2012
%@ 0362-1588
%U https://hdl.handle.net/20.500.14352/42222
%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 crosscap number and denoted by σ˜(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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