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 __________.
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:
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,