### All Abstract Algebra Resources

## Example Questions

### Example Question #1 : Abstract Algebra

Which of the following is an identity element of the binary operation ?

**Possible Answers:**

**Correct answer:**

Defining the binary operation will help in understanding the identity element. Say is a set and the binary operator is defined as for all given pairs in .

Then there exists an identity element in such that given,

Therefore, looking at the possible answer selections the correct answer is,

### Example Question #1 : Introduction

Which of the following illustrates the inverse element?

**Possible Answers:**

**Correct answer:**

For every element in a set, there exists another element that when they are multiplied together results in the identity element.

In mathematical terms this is stated as follows.

For every such that where and is an identity element.

### Example Question #1 : Abstract Algebra

identify the following definition.

Given is a normal subgroup of , it is denoted that when the group of left cosets of in is called __________.

**Possible Answers:**

Subgroup

Cosets

Simple Group

Normal Group

Factor Group

**Correct answer:**

Factor Group

By definition of a factor group it is stated,

Given is a normal subgroup of , it is denoted that when the group of left cosets of in is called the factor group of which is determined by .

### Example Question #4 : Abstract Algebra

Determine whether the statement is true of false:

**Possible Answers:**

True

False

**Correct answer:**

True

This statement is true based on the following theorem.

For all , in .

If is a normal subgroup of then the cosets of forms a group under the multiplication given by,

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