Equation 677 Database

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Magma 70ad4c3322b3…

magma 70ad4c3322b3
Size
121
Isomorphism class hash
70ad4c3322b3bd28fd0cfb48595a85ac48d0aa988849d4dec29f849141317798
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:41
Display reorder
107,1,108,104,103,0,106,105,2,120,109,69,81,84,3,40,117,55,58,93,28,24,113,4,25,90,65,59,77,99,41,34,51,60,86,57,26,119,95,5,42,71,30,73,101,27,79,53,61,38,92,67,115,36,6,39,49,7,75,97,63,23,111,62,32,88,56,94,70,18,15,82,8,43,85,29,118,78,19,114,66,52,44,100,91,16,35,9,45,72,10,110,74,87,20,17,48,31,96,83,116,102,11,46,13,68,54,80,37,21,14,12,22,98,89,50,112,76,47,33,64 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=2 / 4×α=8. • α = 2 on 8 parallel classes (slopes {2, 4, 5, 6, 7, 9, 10, INF}) • α = 8 on 4 parallel classes (slopes {0, 1, 3, 8}) 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=2) 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 11:45:48 · history