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: What is the order of (R240 , R180L) in H⨁K ?

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: What is the order of (R240 , R180L) in 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 where R₁₂₀ is a counterclockwise rotation of 120°, and K be the subgroup of G generated by R₁₈₀L where L is a reflection.

Problem:

What is the order of (R₂₄₀ , R₁₈₀L) in 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
Updated the introduction of the problem. It was messed up. 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: What is the order of L R60 in G?
The introduction of the problem was messed up, and I had to update it. Please help me with this problem. Write it on a piece of paper and upload it here. 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: What is (L R60)-1 in G?
Hello, can you help me out with this problem? Please write a solution on a piece of paper and upload it here. 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
Hello, can you help me out with this problem? Please write a solution on a piece of paper and upload it here. 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: 1. Find an isomorphism from H to ℤ3
Find all homomorphic images of dihedral group, D3.
Hello, can you help me out with this problem? Please write a solution on a piece of paper and upload it here. 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: What is (L R60)-1 in G?