Equation 677 Database

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Magma 4513afb2cc29…

magma 4513afb2cc29
Size
121
Isomorphism class hash
4513afb2cc29dc2099571458ccd6bcb7e98920bc4fcca4b9fb975826285d48b2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:50
Display reorder
69,0,43,98,22,42,51,10,7,116,1,2,70,92,8,9,111,106,67,93,72,33,64,60,89,3,113,35,95,74,25,108,48,61,19,45,26,39,103,49,118,4,53,100,76,96,46,50,5,20,114,29,54,56,40,101,77,90,36,30,57,75,6,104,65,119,110,41,47,21,105,102,24,55,14,11,15,71,115,91,13,37,12,16,17,66,97,23,52,107,44,38,94,32,27,62,112,59,18,109,34,88,117,63,58,68,99,73,31,28,78,83,120,85,81,79,82,86,80,84,87 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=2 / 4×α=6 / 4×α=8. • α = 2 on 4 parallel classes (slopes {0, 1, 3, 7}) • α = 6 on 4 parallel classes (slopes {4, 5, 10, INF}) • α = 8 on 4 parallel classes (slopes {2, 6, 8, 9}) 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=2) operation. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:50 · history