Let Fn be a cyclotomic extension of Q of order n. (a) Determine Aut Q F 5
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Let Fn be a cyclotomic extension of Q of order n.
(a) Determine AutQF5 and all intermediate fields.
(b) Do the same for F8.
(c) Do the same for F7; if ζ is a primitive 7th root of unity what is the irreducible polynomial over Q of ζ+ ζ-1?
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a The extension F5 is a degree 4 extension of Q so any automorphism of F5 fixing Q must send a primitive 5th root of unity to another primitive 5th ro...View the full answer
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Deepak Sharma
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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