Please help.....

For the following sets, with the binary operation given, determine whether or not it forms a group, by checking the group axioms.

(R,◦),where x◦y=(xy)/√3

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- Nov 5th 2013, 04:43 AMFairmum2013Group axioms
Please help.....

For the following sets, with the binary operation given, determine whether or not it forms a group, by checking the group axioms.

(R,◦),where x◦y=(xy)/√3 - Nov 5th 2013, 05:37 AMSlipEternalRe: Group axioms
What are the group axioms? First, you need an identity element: . By cancellation, we find . Next, check that associativity holds:

This follows from associativity and commutativity of real numbers.

Next, check that each element has an inverse. Let . You want to find so that . So, . Solving for we find . Hence, exists so long as .

So, no, it is not a group, but is a group. - Nov 5th 2013, 02:02 PMFairmum2013Re: Group axioms
Much appreciated!!!!! I couldn't figure out the inverse.