Hi SageMath Community,

I'm Sudarshan Dandgawal, a computer engineering student interested in 
contributing to SageMath through Google Summer of Code (GSoC) 2025. I have 
been exploring Issue #34504, which addresses inconsistencies in 
direct_product, semidirect_product, and direct_product_permgroups for 
permutation groups.

Currently, these methods do not properly retain the original domains of the 
input groups when computing their products. This leads to incorrect 
behavior, especially when the groups operate on disjoint domains. My 
proposed solution involves:

   1. 
   
   Ensuring the resulting permutation group correctly reflects the union of 
   the original domains.
   2. 
   
   Implementing relabeling mechanisms to maintain consistency.
   3. 
   
   Adding comprehensive test cases to verify correctness.
   
I would like to know if this issue could be considered as a suitable GSoC 
2025 project. If so, I would be happy to draft a detailed proposal around 
it. Additionally, I’d appreciate any insights from the community regarding:

   - 
   
   Potential challenges or edge cases I should consider while working on 
   this.
   - 
   
   Preferred approaches for handling domain mapping and relabeling.
   - 
   
   Any other guidance to ensure my proposal aligns well with SageMath’s 
   development goals.
   
Looking forward to your feedback and suggestions!

Best regards,
Sudarshan Dandgawal

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