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Let G= Do be the dihedral group of order 12, H be the subgroup of G generated by R120 where R120 is a counterclockwise rotation of 120°, and K be the subgroup of G generated by R180L where L is a reflection. 1. List all elements of G, H, K 2. What is the order of L R60 in G?

Let G= Do be the dihedral group of order 12, H be the subgroup of G generated by R120 where R120 is a counterclockwise rotation of 120°, and K be the subgroup of G generated by R180L where L is a reflection. 1. List all elements of G, H, K 2. What is the order of L R60 in G?

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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6 Let G= Dº be the dihedral group of order 12, H be the subgroup of G generated by R120 where R₁20 is a counterclockwise rotation of 120°, and K be the subgroup of G generated by R180L where L is a reflection. 1. List all elements of G, H, K 2. What is the order of L R60 in G? 1
Transcribed Image Text:6 Let G= Dº be the dihedral group of order 12, H be the subgroup of G generated by R120 where R₁20 is a counterclockwise rotation of 120°, and K be the subgroup of G generated by R180L where L is a reflection. 1. List all elements of G, H, K 2. What is the order of L R60 in G? 1
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