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oai:docta.ucm.es:20.500.14352/422222024-07-11T13:30:17Zcom_20.500.14352_14col_20.500.14352_15

The symmetric crosscap number of the families of groups DC3 × Cn and A4 × Cn Etayo Gordejuela, José Javier Gromadzki, G. Martínez García, Ernesto 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. 2023-06-20T00:13:23Z 2023-06-20T00:13:23Z 2023-06-20T00:13:23Z 2012 journal article https://hdl.handle.net/20.500.14352/42222 0362-1588 metadata only access University of Houston