A classification of regular maps with Euler characteristic a negative prime cube.

Autor: Tian, Yao, Li, Xiaogang
Zdroj: Journal of Algebraic Combinatorics; Dec2024, Vol. 60 Issue 4, p1071-1088, 18p
Abstrakt: For an odd prime p ≥ 5 , all regular maps M on non-orientable surfaces with Euler characteristic - p 3 are classified. Explicitly, it is proved that either M has type { 4 , m } and Aut (M) ≅ (Z 2 × Z 2) ⋊ D 2 m , where m ≡ 3 (mod 6) and m - 4 = p 3 ; or M has type { 2 m , 2 n } and Aut (M) ≅ D 2 m × D 2 n , where 1 < m < n , 2 ∤ m , gcd (m , n) = 1 and m n - m - n = p 3 . In particular, there exists no such map provided p ≡ 1 (mod 12) . [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
Externí odkaz: