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10.3.7. As usual let D8 g² = e, gf H = = = (a,b | a4 = b² = e, ba f2g). Let G {e} x D8 ≤ G. (a) What is o(x)? = (b) Find Hx. What is |G: H|? a³b) and D6 = D6D8. Let x = {f,g | ƒ³ = (f, a) Є G, and let Is H

10.3.7. As usual let D8 g² = e, gf H = = = (a,b | a4 = b² = e, ba f2g). Let G {e} x D8 ≤ G. (a) What is o(x)? = (b) Find Hx. What is |G: H|? a³b) and D6 = D6D8. Let x = {f,g | ƒ³ = (f, a) Є G, and let Is H

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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10.3.7. As usual let D8 g² = e, gf H = = = (a,b | a4 = b² = e, ba f2g). Let G {e} x D8 ≤ G. (a) What is o(x)? = (b) Find Hx. What is |G: H|? a³b) and D6 = D6D8. Let x = {f,g | ƒ³ = (f, a) Є G, and let Is H<G? If the answer is yes, find a familiar group that is isomorphic to G/H? (d) Let y = (e,a). What is CG(y)|? What is clg(y)|? (e) Let PЄ Syl2(G). What is |P|? What is |G: P|? (f) Find one Sylow 3-subgroup of G.
Transcribed Image Text:10.3.7. As usual let D8 g² = e, gf H = = = (a,b | a4 = b² = e, ba f2g). Let G {e} x D8 ≤ G. (a) What is o(x)? = (b) Find Hx. What is |G: H|? a³b) and D6 = D6D8. Let x = {f,g | ƒ³ = (f, a) Є G, and let Is H<G? If the answer is yes, find a familiar group that is isomorphic to G/H? (d) Let y = (e,a). What is CG(y)|? What is clg(y)|? (e) Let PЄ Syl2(G). What is |P|? What is |G: P|? (f) Find one Sylow 3-subgroup of G.
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