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The symmetric genus of the fischer group Fi23

✍ Scribed by Robert A. Wilson

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 127 KB
Volume: 36
Category: Article
ISSN: 0040-9383
DOI: 10.1016/0040-9383(96)00022-5

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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)?

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## 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