All Abstract Algebra Resources
Example Questions
Example Question #1 : Introduction
Which of the following is an identity element of the binary operation ?
Defining the binary operation will help in understanding the identity element. Say
is a set and the binary operator is defined as
for all given pairs in
.
Then there exists an identity element in
such that given,
Therefore, looking at the possible answer selections the correct answer is,
Example Question #2 : Introduction
Which of the following illustrates the inverse element?
For every element in a set, there exists another element that when they are multiplied together results in the identity element.
In mathematical terms this is stated as follows.
For every such that
where
and
is an identity element.
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 __________.
Cosets
Factor Group
Subgroup
Normal Group
Simple Group
Factor Group
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 #1 : Structure Theory
Determine whether the statement is true of false:
True
False
True
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,
All Abstract Algebra Resources
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