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I want a list of Group Theory results that are generally helpful for solving problems in Galois theory, specially, problems involving the Fundamental Theorem of Galois Theory?

The exams are near, and I don`t have enough time to revise Group theory.

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If you can't remember group theory, you're not going to do well anyway, so what good is a list of theorems? – Arturo Magidin Feb 17 '12 at 20:32
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This is a rather pointless question... – Mariano Suárez-Alvarez♦ Feb 17 '12 at 20:39

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1 Answer

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Seems like a fool's errand. The "most useful theorems" are the basic theorems of Group Theory:

  1. Lagrange's Theorem.
  2. Cauchy's Theorem.
  3. Index and counting theorems.
  4. Isomorphism Theorems.
  5. Basic theorems on group actions (since the Galois group acts on the set of roots).
  6. Class equation.
  7. Sylow Theorems.

In short: pretty much every major theorem you cover in a basic, one-semester, Group Theory class that is likely to be a prerequisite for Galois Theory.

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