# basic group theory Q

• Oct 7th 2011, 07:21 PM
sfspitfire23
basic group theory Q
Guys, I took abstract algebra a few years back and I'm trying to refresh my memory. Heres a Q:

True or False: If (G, ∗) is a group that has two or more elements , then the binary operation ∗ is a bijection from G × G to G.

I think sometimes true. Wouldn't the identity*identity=identity? But then I'm sure there are other examples of non identity elements when multiplied equaling the same number and thus not a bijection.

Anyone think of examples?
• Oct 7th 2011, 07:56 PM
Deveno
Re: basic Q
GxG has how many elements?
• Oct 7th 2011, 08:05 PM
sfspitfire23
Re: basic Q
I think greater than two...been awhile, does this make sense?
• Oct 7th 2011, 08:29 PM
Deveno
Re: basic Q
GxG has |G|^2 elements (so 4 if |G| = 2, 9 if |G| = 3, etc...)

how can there possibly be a bijection between GxG and G?
• Oct 9th 2011, 05:42 AM
sfspitfire23
Re: basic Q
but what if G is not finite (i.e. both G x G and G have an infinite number of elements), then we can't use that argument?
• Oct 9th 2011, 10:31 AM
CaptainBlack
Re: basic Q
Quote:

Originally Posted by Deveno
GxG has how many elements?

Please quote the question and preferably whatever post you are replying to, that way we do not need to worry so much about the original questions being deleted, and it is easier to follow what your post is about.

CB