Finite Fields Quiz

A finite field is a field that contains:

• A finite number of elements

• Infinitely many elements

• Only rational elements

• Only complex elements

The order of any finite field is always:

• A composite number

• A power of a prime

• A factorial

• A square root of a prime

Every finite field has:

• Prime characteristic

• Characteristic zero

• Complex numbers

• Transcendental numbers

All finite fields of the same order are:

• Non-isomorphic

• Unique up to isomorphism

• Not fields

• Subfields of Q

The multiplicative group of a finite field is:

• Infinite

• Cyclic

• Trivial

• Non-abelian

The minimal polynomial of an element in a finite field is:

• Reducible

• Irreducible over the base field

• Always linear

• Not unique

The number of elements in F4:

• 4

• 2

• 8

• 16

A generator of the multiplicative group of a finite field is called a:

• Prime element

• Primitive element

• Unity

• Zero

The field F8 has:

• Characteristic 2

• 3 elements

• Order 4

• No additive identity

The order of the multiplicative group of F13 is:

• 13

• 12

• 14

• 6