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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 64E
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Question
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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