期刊
JOURNAL OF PURE AND APPLIED ALGEBRA
卷 228, 期 5, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.jpaa.2023.107561
关键词
Galois theory; Function fields; Ramification
This paper proves the existence of a Galois extension with ramification only at infinity for symmetric and alternating groups over finite fields of odd characteristic.
We prove that for any prime p > 2, q = p(nu) a power of p, n >= p and G = S-n or G = A(n) (symmetric or alternating group), there exists a Galois extension K/F-q(T) ramified only over infinity with Gal(K/F-q(T)) = G. This confirms a conjecture of Abhyankar for the case of symmetric and alternating groups over finite fields of odd characteristic.(c) 2023 Elsevier B.V. All rights reserved.
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