Re: Simple Group Theory Questions
- From: Brian VanPelt <bvanpelt@xxxxxxxxxx>
- Date: Fri, 30 Dec 2005 07:20:36 GMT
On 29 Dec 2005 22:58:51 -0800, animea@xxxxxxxxx wrote:
>Hi,
>I'm self-studying group theory, and I couldn't solve a few of the
>exercises.
>Any hints on how to get them is highly appreciated.
>The questions are:
>
>1- Let G be a group such that for all x in G, x^2=e (e being the
>identity element). Prove G is abelian.
>
>2- Let S be a set and / an operation that assigns to each ordered pair
>(a,b) an element a/b of S, such that:
> a. there is an element a in S such that a/b=1 if and only if a=b;
> b. for any elements a,b,c in S, (a/b)/(b/c)=(a/b)
>Prove that S is a group under the product defined by ab=(a/(1/b)).
>
>I'd prefer some simple hints on how to approach them, rather than
>complete proofs, because i'd like to solve them myself.
>
>Thanks a lot.
On number 1, play with the following equation
x y = x y e
I promise, you will have fun for a long time, but if you play with it
long enough, you will get the answer.
Brian
.
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- Simple Group Theory Questions
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