Homomorphism Quiz

What is a homomorphism?

• A type of group operation

• A mapping between two groups

• A property of numbers

• A method of solving equations

What does the term 'homos' mean in Greek?

• Different

• Form

• Same

• Shape

What is the kernel of a homomorphism?

• The inverse of a function

• The identity element of a group

• The set of elements that map to the identity

• The operation of the group

If a homomorphism is a bijection, what is it called?

• Endomorphism

• Isomorphism

• Epimorphism

• Automorphism

What is the operation used in the group G in the example?

• Division

• Addition

• Multiplication

• Subtraction

What is the identity element in the group H in the example?

• i

• 0

• -1

• 1

What does the mapping f(x) = i^x represent?

• A constant function

• An identity function

• A function from H to G

• A function from G to H

What is a property of homomorphisms?

• They can only map finite groups

• They can only map integers

• They preserve group operations

• They are always injective

What is the result of f(x + y) in the example?

• f(x) + f(y)

• f(x) * f(y)

• f(x) - f(y)

• f(x) / f(y)

What is the notation for the kernel of a homomorphism?

• KerΦ

• Hom(G, H)

• Φ(G)

• G*H