CH 4 - Finite Fields

Question 1

State a subfield property of finite F with characteristic p.

|F| = ?

Answer 1

Question 2

Freshman’s Exponentiation

State and prove a lemma of three properties of finite fields with order p^n.

State a theorem on existence and uniqueness of fields of order p^n.

Answer 2

Question 3

Define the Galois field of order p^n.

State a theorem with two properties of finite fields.

Answer 3

Question 4

Define the exponent of a finite group.

State a lemma on finite abelian groups and exponents.

State a theorem on the multiplicative group of a finite field.

State a corollary on finite and simple extensions.

Answer 4