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Understanding Homomorphisms and Kernels

Understanding Homomorphisms and Kernels

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Jennifer Brown

FREE Resource

5 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a homomorphism between two groups?

A function that maps elements from one group to another while preserving group operations

A function that is always one-to-one

A function that maps elements from one group to another without any specific properties

A function that is always onto

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a homomorphism send identity elements to?

Random elements

Identity elements

Kernel elements

Inverse elements

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why do homomorphisms send inverses to inverses?

Because inverses are not important in group theory

Because it is a property of homomorphisms to preserve group operations

Because inverses are always mapped to identity elements

Because inverses are mapped to random elements

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the kernel of a homomorphism?

A subset of the codomain group

A measure of how a homomorphism fails to be one-to-one

A random collection of elements

A set of elements that map to random elements in the codomain

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is true about the kernel of a homomorphism?

It is always empty

It is a subgroup of the codomain group

It is a subgroup of the domain group

It contains only the identity element of the codomain

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