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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)?


Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
50 KB
Volume
93
Category
Article
ISSN
0012-365X

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✦ 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,,)?


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