Equation 677 Database

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Magma b62281e320c0…

magma b62281e320c0
Size
121
Isomorphism class hash
b62281e320c092a243c78e8473cb6faa2b70ef055297d73876acd0f4fa417ee1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:36
Display reorder
0,120,58,12,1,13,42,10,59,43,11,87,77,2,45,102,113,23,64,15,74,94,36,78,14,116,52,89,41,68,3,106,82,114,9,109,4,46,26,95,103,75,60,88,90,8,37,27,117,5,83,53,107,69,32,98,31,112,101,63,86,16,73,44,6,22,81,30,93,51,67,35,7,105,115,17,40,57,18,96,76,28,20,84,47,61,99,110,29,19,79,108,56,38,33,118,70,54,91,21,25,85,62,72,97,111,49,100,48,65,39,24,34,71,104,80,92,66,55,119,50 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): 4×α=6 / 8×α=7. • α = 6 on 4 parallel classes (slopes {3, 4, 5, INF}) • α = 7 on 8 parallel classes (slopes {0, 1, 2, 6, 7, 8, 9, 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=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 11:45:56 · history