To state whether the group in exercises 3 and 4 are commutative or not.
Answer to Problem 6E
Yes, the group in exercises 3 and 4 are commutative.
Explanation of Solution
Given information: A symmetry group is called commutative if
The symmetry group of the table as shown below,
| I | | | |
I | I | | | |
| | I | | |
| | | I | |
| | | | I |
The table of exercise 3 are as follow,
| I |
I | I |
The table of exercise 4 are as follow,
| I |
I | I I I |
From the above table the commutative rule is applicable,
Therefore,
Thegroup in exercises 3 and 4 are commutative.
Chapter 14 Solutions
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