2026-07-07T04:40:40Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/422222024-07-11T13:30:17Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Etayo Gordejuela, José Javier
author
Gromadzki, G.
author
Martínez García, Ernesto
2023-06-20T00:13:23Z
2023-06-20T00:13:23Z
2012
0362-1588
https://hdl.handle.net/20.500.14352/42222
http://math.uh.edu/~hjm/restricted/pdf38(2)/02gordejuela.pdf
http://math.uh.edu/
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.
The symmetric crosscap number of the families of groups DC3 × Cn and A4 × Cn
journal article