CLASSIFICATION OF BI-DIHEDRAL MAPS OF NEGATIVE PRIME CHARACTERISTIC

Širáň et al. gave a classification of bi-rotary maps on non-orientable surfaces with a negative odd prime Euler characteristic in 2019. There are 14 types of edge transitive maps. The bi-dihedral map is also one of the 14 types of edge transitive maps. Let M be a bi-dihedral map, with χ(M) = −p for an odd prime number p, and G = Aut(M). The main result of this thesis shows that: if p divides the order of G, then G is exactly one of S_4,A_5 or Z_3 : S_3, and if p does not divide the order of G, then G = D_2n.

在2019年，Širáň 等人给了不可定向曲面上欧拉特征为奇素数的双旋转地图一个分类。 边传递地图可分为14类。 双二面体地图也是其中的一类。 令 M 为一个双二面体地图，且欧拉特征 χ(M) = −p 这里 p 是奇素数, G = Aut(M)。文章的主要结果证明了: 如果 p 整除群 G 的阶， 那么 G S_4, A_5 或 Z_3 : S_3 其中之一, 如果 p 不整除群 G 的阶, 那么 G = D_2n。