- #1
nigelscott
- 135
- 4
Homework Statement
I am looking at the quotient group G = Z/3Z which is additive and abelian. The equivalence classes are:
[0] = {...,0,3,6,...}
[1] = {...,1,4,7,...}
[2] = {...,2,5,8,...}
I want to prove [0] is a normal subgroup, N, by showing gng-1 = n' ∈ N for g ∈ G and n ∈ N. Since G is abelian so gg-1n = n' ∈ N. The identity element 0 is also in G so I should be able to write 0.0-1n = n'. How do I interpret 0.0-1?
Homework Equations
The Attempt at a Solution
My first thought was that since the inverse of the identity is the identity then 0.0<sup>-1</sup> = 0. Therefore, this would give 0n = n' = 0. This is also consistent with 0n = n0. However, I am still not sure about this because the identity is being used multiplicatively and not additively.