Proposal for Improving direct product and Related Methods in Permutation Groups (Issue #34504)

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Sudarshan Dandgawal

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Mar 27, 2025, 8:17:09 AMMar 27

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Hi everyone,

I'm Sudarshan Dandgawal, a student preparing my Google Summer of Code (GSoC) proposal for SageMath. 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 results when working with groups on disjoint domains. My proposed solution involves:

Ensuring the resulting permutation group correctly reflects the union of the original domains.
Implementing proper relabeling mechanisms to maintain consistency.
Adding test cases to verify correctness.

I'd love to get feedback from the community on my approach before finalizing my GSoC proposal. Specifically:

Are there edge cases I should consider when modifying these methods?
Would a specific implementation strategy be preferred for handling domain mappings?
Any additional insights or potential challenges I should be aware of?

I’d greatly appreciate any thoughts, suggestions, or guidance on refining my proposal. Looking forward to your feedback!