Problem 141. : The genus of a Cayley graph is the smallest genus of any surface on which the graph can be imbedded. The genus of a group G is the smallest genus of all connected Cayley graphs on G. Is it true that for each genus g, there is a group of genus g?

Problem 142. : The symmetric genus of a

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)?

📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 50 KB

## 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 leas

Problem 141. : The genus of a Cayley graph is the smallest genus of any surface on which the graph can be imbedded. The genus of a group G is the smallest genus of all connected Cayley graphs on G. Is it true that for each genus g, there is a group of genus g?

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