# Group Theory: Equivalence relations?

Let G be a group. Define a relation ~ on the elements of G as follows:
a ~ b <=> a = gbg^(-1) for some element g in G.
Now, suppose that G = D3 (the dihedral group of order 6)
Compute the equivalence class of R120:
**Now I've found that the elements of D3 = {R0,R120,R240,F1,F2,F3}, where each...
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Let G be a group. Define a relation ~ on the elements of G as follows:

a ~ b <=> a = gbg^(-1) for some element g in G.

Now, suppose that G = D3 (the dihedral group of order 6)

Compute the equivalence class of R120:

**Now I've found that the elements of D3 = {R0,R120,R240,F1,F2,F3}, where each R_ represents a counterclockwise rotation the amount of degrees associated and each F_ represents a flip(reflection) about one of the three diagonals. I'm just not sure how to perform the rest.

I've done the other portions of the question: proving the equivalence relation and describing the equivalence classes of G under ~ if G is abelian. But, for some reason this just loses me, maybe because it's not just strictly number, I don't know....

Please Help!!!

a ~ b <=> a = gbg^(-1) for some element g in G.

Now, suppose that G = D3 (the dihedral group of order 6)

Compute the equivalence class of R120:

**Now I've found that the elements of D3 = {R0,R120,R240,F1,F2,F3}, where each R_ represents a counterclockwise rotation the amount of degrees associated and each F_ represents a flip(reflection) about one of the three diagonals. I'm just not sure how to perform the rest.

I've done the other portions of the question: proving the equivalence relation and describing the equivalence classes of G under ~ if G is abelian. But, for some reason this just loses me, maybe because it's not just strictly number, I don't know....

Please Help!!!

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