11. Let K be the splitting field of x³ – 2 over Q. (Refer to Example 50.9.) a. Describe the six elements of G(K/Q) by giving their values on 2 and i/3. (By Example 50.9, K = QWZ, i /3).) b. To what group we have seen before is G(K/Q) isomorphic? c. Using the notation given in the answer to part (a) in the back of the text, give the diagrams for the subfields of K and for the subgroups of G(K/Q), indicating corresponding intermediate fields and subgroups, as we did in Fig. 53.4.
11. Let K be the splitting field of x³ – 2 over Q. (Refer to Example 50.9.) a. Describe the six elements of G(K/Q) by giving their values on 2 and i/3. (By Example 50.9, K = QWZ, i /3).) b. To what group we have seen before is G(K/Q) isomorphic? c. Using the notation given in the answer to part (a) in the back of the text, give the diagrams for the subfields of K and for the subgroups of G(K/Q), indicating corresponding intermediate fields and subgroups, as we did in Fig. 53.4.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Section 53 number 11
Transcribed Image Text:gen
ator öf the group G(GF(729)/GF(9)).
11. Let K be the splitting field of x³ – 2 over Q. (Refer to Example 50.9.)
a. Describe the six elements of G(K/Q) by giving their values on 2 and i/3. (By Example 50.9, K =
QWZ, i/3).)
b. To what group we have seen before is G(K/Q) isomorphic?
c. Using the notation given in the answer to part (a) in the back of the text, give the diagrams for the subfields
of K and for the subgroups of G(K/Q), indicating corresponding intermediate fields and subgroups, as we
did in Fig. 53.4.
Transcribed Image Text:{1,01, 02, 03}
{1, 01}
{1, 02}
{t, 03)
{1}
(а)
Q(/2, v3) = K}
K.a,) = Q(/3)
Q(/2) = K, a,)
Q(W6) = K, 0,)
%3|
Q= K, 0, 0, 03)
(b)
53.4 Figure
(a) Group diagram. (b) Field diagram.
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