Introduction of the problem: Let G = D6 be the dihedral group of order 12, H be the subgroup of G generated by R120 rotation of 120°, and K be the subgroup of G generated by where R120 is a counterclockwise R180L where L is a reflection. Problem: List all elements of G, H, K

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 45E: 45. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )
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Introduction of the problem:

Let G = D6 be the dihedral group of order 12, H be the subgroup of G generated by R120 rotation of 120°, and K be the subgroup of G generated by where R120 is a counterclockwise R180L where L is a reflection.

Problem:

List all elements of G, H, K

 

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The introduction of the problem was messed up, and I had to update it. Please help me with this problem. Write the solution on a piece of paper and upload it here. Thank you!

Introduction of the problem:

Let G = D6 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.

Problem:

List all elements of G, H, K

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