Equation 677 Database

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Magma ab07f9801f41…

magma ab07f9801f41
Size
121
Isomorphism class hash
ab07f9801f4167faea23486a9b4224c2ba8ceca89c3bb69b5058825efc89286e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:04
Display reorder
1,22,23,3,24,20,0,4,120,2,21,16,5,65,82,87,46,37,112,102,50,10,110,11,6,48,63,85,17,80,100,35,108,78,106,12,43,7,71,118,56,98,18,83,54,91,104,19,13,8,76,41,96,116,69,39,67,89,114,109,14,52,15,94,74,9,86,49,81,25,111,58,45,64,101,30,36,72,44,57,31,79,119,84,26,99,107,59,27,60,42,105,55,77,70,32,97,92,117,33,115,61,90,40,53,28,103,95,68,75,47,73,113,66,62,38,34,88,93,29,51 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=7. • α = 2 on 8 parallel classes (slopes {1, 3, 6, 7, 8, 9, 10, INF}) • α = 7 on 4 parallel classes (slopes {0, 2, 4, 5}) 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=7) operation. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:51 · history