Problem 142. : The symmetric genus of a group G is the minimum genus of a surface on which G acts. Let An denote the alternating group of degree n, γG denote the genus of the group G, and σ(G) the symmetric genus of G. Is the following conjecture true? Conjecture: For at least one n, γ(An)<σ(An)?

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 50 KB
• Volume: 93
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(91)90224-p

✦ Synopsis

Reseirrch problems

Problem 142. The symmetric genus of a group G is the minimum genus of a surface on which G acts. Let A, denote the alternating group of degree n, y(G) denote the genus of the group G, and a(G) the symmetric genus of G. Is the following conjecture true? Conjecture: For at least one n, y(A,l) c a(A,,)?