- #1
facepalmer
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Homework Statement
Taking the Dih(12) = {α,β :α6 = 1, β2 = 1, βα = α-1β}
and a function Nr = {gr: g element of Dih(12)}
Homework Equations
Taking the above I have to find the elements of N3. And then prove that N3 is not a subgroup of Dih(12).
The Attempt at a Solution
For N3 I have determined the following are elements. 1, α3, β, βα3.
Now to attempt to prove whether these elements form a subgroup of Dih(12) I created the multiplication table. The result was the table was closed and so I would assume that the aforementioned subset is a subgroup.
I assume I have done one of two things wrong; either
a) My understanding of generating n3 is misguided, though if I take an element of Dih(12), say αβ, and then using the function defined I get (αβ)3 = α3ββ = α3.
or b) my multiplication table is wrong.
Any help on what my mistake is is appreciated.