Fundamental theorem of galois theory

Assignment Help Algebra

Reference no: EM13118644

Suppose K is a Galois extension of F of degree p^n for some prime p and some n >= 1. Show that there are Galois extensions of F contained in K of degree p and p^(n-1).

Note: It is assumed that you know the following results in order to prove this theorem.

You may search for the proofs of these results.

1. G = Aut_F(K) has a subgroup of order p^(n-1)

2. The Fundamental Theorem of Galois Theory

3. Cauchy's Theorem

Reference no: EM13118644

Questions Cloud

Use of system of inequalities : Develop a word problem that requires the use of the system of inequalities? The answer to the problem must be presented in graphical and algebraic forms.

Explain the fair price to play the game : The fair price to play the game. A person spins the pointer and is awarded the amount indicated by the pointer. The wheel has three amounts to win

How many true-breeding varieties of squash : A variety of squash may be long, round, or oval in shape. The color may be yellow, green, or white. A long, white variety crossed with a round, green one (both true-breeding) produces only oval, yellow F1's.

How many times heavier is a molecule : Each of 2 front tire in the car is filled with a different gas. One tire contains 116g of helium, another tire has 160g of unknown gas. How many times heavier is a molecule of the unkown gas than an atom of helium.

Fundamental theorem of galois theory : Suppose K is a Galois extension of F of degree p^n for some prime p and some n >= 1. Show that there are Galois extensions of F contained in K of degree p and p^(n-1).

What molecule is produced in the citric acid : What molecule is produced in the citric acid cycle as a by-product of glucose oxidation and is subsequently released into the bloodstream and carried to the lungs, where it is removed from the body?

Write an essay on Domestic violence : Write an essay on Domestic violence, properly cited and references should clear for it.

Make a tree diagram to represent this situation : Construct a tree diagram to represent this situation. A mini license plate for a toy car must consist of a vowel followed by two numbers. Each number must be a 3 or 7.

Two solutions in quadratic equations : Why are there usually two solutions in quadratic equations? Under what situation would one or more solutions of a rational equation be unacceptable?

User Account

All Pages