For each finite group G with |G|≤7, give an example of an equation whose Galois group over Q is isomorphic to G.
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Originally Posted by apple2009 For each finite group G with |G|≤7, give an example of an equation (polynomial over Q?) whose Galois group over Q is isomorphic to G. See 1 and 2. For example, a corresponding polynomial over Q for a galois group of order 4 is x^5-1 since $\displaystyle |(\mathbb{Z}/5\mathbb{Z})^\times|=4$. For an order 3, you might need to use A_3=Z_3. You can find the corresponding polynomial in the above link.
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