RT Journal Article
T1 The symmetric crosscap number of the families of groups DC3 × Cn  and A4 × Cn
A1 Etayo Gordejuela, J. Javier
A1 Gromadzki, G.
A1 Martínez García, Ernesto
AB 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.
PB University of Houston
SN 0362-1588
YR 2012
FD 2012
LK https://hdl.handle.net/20.500.14352/42222
UL https://hdl.handle.net/20.500.14352/42222
DS Docta Complutense
RD 7 may 2024