Problem

Let G be the set of all polynomials of the form ax2 + bx + c with coefficients from the...

Let G be the set of all polynomials of the form ax2 + bx + c with coefficients from the set {0, 1, 2}. We can make G a group under addition by adding the polynomials in the usual way, except that we use modulo 3 to combine the coefficients. With this operation, prove that G is a group of order 27 that is not cyclic.

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