Equation 677 Database

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Magma 83a10ff448e0…

magma 83a10ff448e0
Size
121
Isomorphism class hash
83a10ff448e020055ba954f21047deb23d4965798dd069bcd1f5a2550f10bfa9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:37
Display reorder
61,26,9,27,120,1,60,5,0,4,8,2,13,88,99,90,79,119,6,106,28,23,111,73,22,12,35,30,3,29,95,7,42,51,58,20,47,34,41,94,67,10,110,72,78,48,103,59,89,11,105,118,87,66,21,70,49,24,97,37,54,53,14,64,44,113,52,76,116,108,92,65,101,85,55,15,25,40,114,31,18,33,71,38,98,16,50,45,39,19,46,117,93,17,86,104,102,77,32,62,43,96,57,36,112,68,81,83,74,109,69,56,107,84,91,82,63,100,115,80,75 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

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 split EVENLY into two line-operation types (in the natural F_11 parameterization x ◇ y = (1-α)x + αy): • 6 parallel classes use α = 6 (the F_11 midpoint quasigroup x ◇ y = 6(x+y) mod 11, which is commutative). • 6 parallel classes use α = 7 (the non-commutative operation x ◇ y = 5x + 7y mod 11). Globally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. The display reorder presents points as (h, v) ∈ F_11 × F_11; all 11 diagonal 11×11 blocks render as the identical F_11(α=6) Cayley table, and the 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation. Compare 985e14d6, which has the same combinatorial AG(2, 11) structure but an uneven 8 × α=6 / 4 × α=8 split. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:48 · history