Equation 677 Database

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Magma d31e0c93a852…

magma d31e0c93a852
Size
121
Isomorphism class hash
d31e0c93a8527e2728dc01cd3ed2f520e44303c78e51949596be178e6014d470
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:48
Display reorder
9,4,1,2,8,120,0,6,7,3,5,73,108,114,81,89,18,26,46,93,10,32,85,11,104,27,99,19,110,33,52,82,69,95,78,12,116,48,15,30,75,34,28,91,44,29,79,106,35,16,13,87,71,112,101,36,118,25,14,77,17,80,97,83,109,50,67,88,72,45,39,57,20,107,113,102,62,40,98,84,21,119,53,68,58,103,51,63,115,47,94,74,37,54,90,64,59,22,41,105,23,43,86,60,55,100,42,65,70,111,61,76,24,96,66,56,49,117,38,92,31 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): 6×α=2 / 6×α=8. • α = 2 on 6 parallel classes (slopes {0, 1, 2, 3, 5, 9}) • α = 8 on 6 parallel classes (slopes {4, 6, 7, 8, 10, INF}) 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=8) 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 11:45:59 · history