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 (Crying)

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- Oct 24th 2010, 11:48 PMDreamer78692Isomorphism
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 (Crying) - Oct 25th 2010, 02:33 AMtonio
- Oct 25th 2010, 10:34 PMDreamer78692
Sorry about that...

R - stands for the Rotation groups

e.g. R3 = {e, r, r^2}

A - Alternating Groups - Oct 26th 2010, 12:57 AMSwlabr
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). - Oct 26th 2010, 04:02 AMtonio
- Oct 26th 2010, 04:34 AMSwlabr
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 $\displaystyle D_3 \cong S_3$. - Oct 26th 2010, 06:06 AMtonio
- Oct 26th 2010, 06:11 AMSwlabr
- Oct 26th 2010, 06:56 AMtonio
- Oct 26th 2010, 08:15 AMMichaelMath
Sorry to go off topic for a moment, but I dream of a day when all mathematical notation and terminology is standardized internationally. Also, I wish they would stop referring to math as "maths" in the UK.

- Oct 27th 2010, 12:08 AMSwlabr