Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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4. Let w = e 11, and let E = Q(w). (a) Verify that [E:Q] 10. (b) Determine |Gal(E/Q)|, the number of automorphisms of E that fix Q. (c) Find the order of y(w) w? in Gal(E/Q). (d) How many subfields K does E have (such that QC K C E)? Hint 1 The corollary to Eisenstein's theorem might help. Hint 2: Example 6, page 535 may help.
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Transcribed Image Text:4. Let w = e 11, and let E = Q(w). (a) Verify that [E:Q] 10. (b) Determine |Gal(E/Q)|, the number of automorphisms of E that fix Q. (c) Find the order of y(w) w? in Gal(E/Q). (d) How many subfields K does E have (such that QC K C E)? Hint 1 The corollary to Eisenstein's theorem might help. Hint 2: Example 6, page 535 may help.
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