Structure Theory - Abstract Algebra
Card 0 of 2
Question
identify the following definition.
Given 
is a normal subgroup of 
, it is denoted that 
when the group of left cosets of 
in 
is called __________.
identify the following definition.
Given
Answer
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 
.
By definition of a factor group it is stated,
Given
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Question
Determine whether the statement is true of false:
Determine whether the statement is true of false:
Answer
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,
This statement is true based on the following theorem.
For all
If
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