Abstract Algebra : Structure Theory

Study concepts, example questions & explanations for Abstract Algebra

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Example Questions

Example Question #1 : Structure Theory

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:

Factor Group

Subgroup

Normal Group

Cosets

Simple Group

Correct answer:

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 #2 : Structure Theory

Determine whether the statement is true of false:

Possible Answers:

False

True

Correct answer:

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,

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