首页> 外文OA文献 >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)?

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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)?

机译：问题142. G组的对称族是G作用于其上的曲面的最小族。设An表示度数的交替组，γG表示组G的属，而σ（G）表示G的对称属。以下猜想是否正确？猜想：对于至少一个n，γ（An）<σ（An）？

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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)?

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