Etayo Gordejuela, J. Javier and Gromadzki, G. and Martínez García, Ernesto (2012) The symmetric crosscap number of the families of groups DC3 × Cn and A4 × Cn. Houston Journal of Mathematics, 38 (2). pp. 345-358. ISSN 0362-1588
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.
|Uncontrolled Keywords:||Klein surfaces; automorphism|
|Subjects:||Sciences > Mathematics > Group Theory|
|Deposited On:||03 Jul 2012 10:13|
|Last Modified:||03 Jul 2012 10:13|
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