(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Exercise 1.2:2.

(i) If G is a group

Define an operation dG on |G| by dG(x, y) = x*y^-1.

Does the group given by (G,dG) determine the original group G with *

(I.e., if G1 and G2 yield the same pair, (G1,dG1) = (G2,dG2) , must G1 = G2?)

There is a part II, but I would rather focus on I first.

3. The attempt at a solution

So, I started by noting that G,dG forces every element to be of order 2 since:

x dG x = x*x^-1 = e = x dG x^-1 thus x^-1 = x

Thus G,dG is a klein group. I'm not sure how to proceed, any hint would be appreciated

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# Homework Help: Groups with new Operations

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