Abstract
We prove that for any prime p>2, q=pν a power of p, n≥p and G=Sn or G=An (symmetric or alternating group), there exists a Galois extension K/Fq(T) ramified only over ∞ with Gal(K/Fq(T))=G. This confirms a conjecture of Abhyankar for the case of symmetric and alternating groups over finite fields of odd characteristic.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
