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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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)
Quote:
Originally Posted by Dreamer78692
What is R4, R3, R12, A3, A4...??
Tonio
Sorry about that...
R - stands for the Rotation groups
e.g. R3 = {e, r, r^2}
A - Alternating Groups
I presume by `rotation group' you meanQuote:
Originally Posted by Dreamer78692
, the group of symmetries of a regular n-gon (Rn=
).
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 thatis abelian but not cyclic).
Quote:
Originally Posted by SwlabrI presume by `rotation group' you mean
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
Very weird notation, but according to it, and if I didn't misunderstood, also (B) is correct since
bothare cyclic groups of order 3...
Tonio
Notation notation notation! However, I do not think you are correct in any notation. I writeQuote:
Originally Posted by tonioVery weird notation, but according to it, and if I didn't misunderstood, also (B) is correct since
both
Tonio
. It is always of even order, and so cannot be cyclic of order 3...
It is true, however, that.
Quote:
Originally Posted by SwlabrNotation notation notation! However, I do not think you are correct in any notation. I write
It is true, however, that
The OP himself, though, wrote thata cyclic group of order 3. Perhaps for him "rotation group" is
ONLY the actual rotations (spinnings) , no the whole dihedral group.
Tonio
Fair point. In which case, (A) is false.Quote:
Originally Posted by tonioThe OP himself, though, wrote that
ONLY the actual rotations (spinnings) , no the whole dihedral group.
Tonio
Quote:
Originally Posted by Swlabr
Indeed, which I think was the case from the beginning, since then one is a cyclic group whereas the other isn't...who knows what the truth is here in Weirdnotationland.
Tonio
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.
That's okay, in the UK we wish they would stop referring to maths as `math' in the US.Quote:
Originally Posted by MichaelMath