Do we have a method to find one (or all) isomorphism between two given magmas with one using GAP?
Edit
If we have Loop or Latin square (with one) instead of Magma then do we have the method?
2026-02-23 03:01:43.1771815703
Isomorphism between two magmas with one.
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The LOOPS package for GAP is designed for finite loops, for which the isomorphism problem is of course very much decidable.
If $L, M$ are finite loops, the method $\operatorname{IsomorphismLoops}(L,M)$ returns an isomorphism from $L$ to $M$, if it exists, else it returns "fail".
To calculate all isomorphisms from $L$ to $M$, it suffices to calculate $\operatorname{AutomorphismGroup}(M)$, and compose the above isomorphism with all elements of the automorphism group.
The methods of the LOOPS package can be modified to find isomorphisms among magmas with 1.