Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 8×α=8.
• α = 2 on 4 parallel classes (slopes {0, 5, 7, 8})
• α = 8 on 8 parallel classes (slopes {1, 2, 3, 4, 6, 9, 10, INF})
Globally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=8) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.
[text written by Claude]
dwrensha · 2026-05-13 11:44:34
Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 8×α=8.
• α = 2 on 4 parallel classes (slopes {0, 5, 7, 8})
• α = 8 on 8 parallel classes (slopes {1, 2, 3, 4, 6, 9, 10, INF})
Globally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=8) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.
dwrensha · 2026-05-13 11:45:49
dwrensha · 2026-05-13 11:44:34