Structure Theory
Help Questions
Abstract Algebra › Structure Theory
Questions 1 - 2
1
identify the following definition.
Given is a normal subgroup of
, it is denoted that
when the group of left cosets of
in
is called __________.
Factor Group
Simple Group
Subgroup
Normal Group
Cosets
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
.
2
Determine whether the statement is true of false:
True
False
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,