Galois and Klein 4: Isomorphic or Cyclic?

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Thread starter morganjp
Start date Dec 12, 2007
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morganjp

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Dec 12, 2007

suppose a +ve degree polynomial g(x) in G[x] with F splits over G and no irr. factor has repeated root. then if [F:G]=4, we know the size of Gal(F/G) is also 4. so it's either isomorphic to the Klein 4 or cyclic group of order 4. is there any trick to tell it's one and not the other?

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morphism

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Dec 12, 2007

The Galois group will permute the roots. Can you find a permutation of order 4?

Galois and Klein 4: Isomorphic or Cyclic?

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Galois and Klein 4: Isomorphic or Cyclic?

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