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Advanced MathQ&A Library82. Let G be the set of all polynomi als of the form ax2 + bx + c withcoefficients from the set {0, 1, 2}. We can make G a group underaddition by adding the polynomi als in the usual way, except thatwe use modulo 3 to combine the coefficients. With this operation,prove that G is a group of order 27 that is not cyclic.Question

Asked Sep 17, 2019

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Step 1

To prove that (1) G is a group or order 27 and (2) G is not a cyclic group

Step 2

(1) By very definition, G is isomorphic to the Cartesian product gro...

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