Which of the following statements is true? (V is the Klein-4 group)
"=" represents isomorphic to.
(A) V = R4
(B) A3=R3
(C) A4=R12
(D) V =Z/4Z
(E) (Z; +) = (Q; +).
My answer was (A)..
Please help
I presume by `rotation group' you mean $\displaystyle D_{n}$, the group of symmetries of a regular n-gon (Rn=$\displaystyle D_n$).
You are correct. What were your thinkings in the other questions? (Order arguments and pointing out cyclic groups when you see them will work). Can you prove your result? (prove that $\displaystyle D_4$ is abelian but not cyclic).
Notation notation notation! However, I do not think you are correct in any notation. I write $\displaystyle D_n$ for the set of symmetries of a regular n-gon, which is also often written as $\displaystyle D_{2n}$. It is always of even order, and so cannot be cyclic of order 3...
It is true, however, that $\displaystyle D_3 \cong S_3$.