All Abstract Algebra Resources
Example Questions
Example Question #3 : 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:
Simple Group
Cosets
Subgroup
Normal Group
Factor 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 #4 : Abstract Algebra
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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