A apple2009 Oct 2009 56 0 May 18, 2010 #1 For each finite group G with |G|≤7, give an example of an equation whose Galois group over Q is isomorphic to G.

For each finite group G with |G|≤7, give an example of an equation whose Galois group over Q is isomorphic to G.

T TheArtofSymmetry May 2010 95 38 May 19, 2010 #2 apple2009 said: 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. Click to expand... 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.

apple2009 said: 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. Click to expand... 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.