This abstract algebra problem seems trivially easy. Did I overlook something?

In summary, it is important to double-check calculations to ensure accuracy, consider alternative solutions, review relevant concepts and theorems, seek help from others, and carefully analyze problems before determining their difficulty.
  • #1
jdinatale
155
0

Homework Statement



trivially.jpg




The problem seems too easy so I suspect that I am overlooking something important. A problem this easy would be completely out of character for my professor...
 
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  • #2
You've shown it's a homomorphism, but it asked you to show it's an isomorphism.
 
  • #3
vela said:
You've shown it's a homomorphism, but it asked you to show it's an isomorphism.

Whoops! That's a typo. I typed the question wrong in latex. The problem on the assignment sheet says homomorphism.

So assuming that the problem is asking for a homomorphism, does it look legit?
 
  • #4
Looks fine to me.
 

1. Did I make a mistake in my calculations?

No, it is possible that the problem may seem easy but the answer is correct. However, it is always a good idea to double-check your calculations to ensure accuracy.

2. Is there a simpler solution that I missed?

There may be multiple ways to solve a problem, so it is possible that there is a simpler solution that you did not consider. It is always helpful to discuss your approach with others to see if there are alternative methods.

3. Am I missing a key concept or theorem?

Abstract algebra problems often involve multiple concepts and theorems, so it is possible that you may have overlooked one that is necessary for this particular problem. It may be helpful to review and make sure you have a solid understanding of the relevant concepts and theorems.

4. Should I seek help from a peer or a professor?

If you are struggling with a problem, it is always a good idea to seek help from others. You can discuss the problem with a peer or seek assistance from your professor. They may be able to offer insights or point out any mistakes you may have made.

5. Is it possible that the problem is actually more difficult than it seems?

Yes, it is possible that the problem may have a clever or non-obvious solution that may make it more difficult than it appears. It is important to carefully analyze the problem and consider all possibilities before concluding that it is easy.

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