# Abstract Algebra : Groups

## Example Questions

### Example Question #1 : Abstract Algebra

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

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,   ### Example Question #1 : Introduction

Which of the following illustrates the inverse element?      Explanation:

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 __________.

Subgroup

Cosets

Simple Group

Normal Group

Factor Group

Factor Group

Explanation:

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: True

False

True

Explanation:

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, ### All Abstract Algebra Resources 