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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
Normal Group
Simple Group
Subgroup
Cosets
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:
True
False
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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