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?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 12E: Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...
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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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