Equation 677 Database

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Magma fd4053a18b9b…

magma fd4053a18b9b
Size
121
Isomorphism class hash
fd4053a18b9bb75d2e0227fe7be95f0dc5edc60a7284fd8c21c333703d038b8d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:39
Display reorder
67,4,15,62,14,68,61,120,0,1,5,70,44,9,105,29,111,78,2,7,92,91,119,90,28,100,8,69,86,3,58,6,45,42,74,107,20,75,94,24,65,10,97,113,60,116,102,25,109,43,21,66,98,11,73,32,76,95,89,18,38,53,12,30,114,108,39,84,19,52,56,33,88,13,117,31,103,79,63,112,93,54,106,36,47,82,50,16,87,17,55,37,115,101,59,46,51,83,64,35,57,71,27,81,22,118,40,85,99,49,23,48,80,110,72,34,26,41,77,104,96 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 partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 8×α=6 / 4×α=7. • α = 6 on 8 parallel classes (slopes {1, 4, 5, 6, 8, 9, 10, INF}) • α = 7 on 4 parallel classes (slopes {0, 2, 3, 7}) 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=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:57 · history