Equation 677 Database

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Magma d2ea11ab0d05…

magma d2ea11ab0d05
Size
121
Isomorphism class hash
d2ea11ab0d0513122e5e98515a73964b27348d2d0356c2250e1513a47ba2ca05
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:31
Display reorder
108,106,105,109,8,0,120,1,2,107,104,102,27,114,86,32,56,71,83,53,15,3,18,112,4,51,87,81,72,33,57,28,103,24,5,99,58,49,29,73,88,79,110,16,113,100,14,82,54,84,69,52,30,6,25,7,17,26,31,80,50,70,55,85,101,111,78,66,23,117,59,46,98,42,37,89,9,90,19,10,38,115,40,94,60,47,64,76,67,11,74,48,34,61,95,118,43,20,91,21,77,92,41,44,116,96,35,62,12,65,13,93,68,63,39,36,97,45,119,75,22 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=7 / 4×α=8. • α = 7 on 8 parallel classes (slopes {2, 3, 4, 5, 6, 8, 9, INF}) • α = 8 on 4 parallel classes (slopes {0, 1, 7, 10}) 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=7) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=8) operation. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:56 · history