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How to determine Galois group of a general monic septic or octic polynomial.Could anyone suggest any reference material like some research paper or book.

Edit:Even a condition to decide the solvability of a septic equation would do.I already know that if it is solvable then it's Galois group is solvable and contained in semi product of Z_7 and Z_6.But I need a condition not related to Galois group as eventuallya I aim to find that only.

Jyoti Yadav
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    Are you familiar with Dedekind's theorem? It gives a lot of information about the cycle types of element of the Galois group when viewed as a group of permutations of the zeros. I don't know if it gives enough information to always ID the group though. – Jyrki Lahtonen Jul 04 '16 at 19:24
  • @JyrkiLahtonen..This works really well in certain cases but wouldn't be of much help for a general criteria to distinguish between various Galois groups. – Jyoti Yadav Jul 05 '16 at 12:35

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