Equation 677 Database

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Magma fa0f52cd7d47…

magma fa0f52cd7d47
Size
121
Isomorphism class hash
fa0f52cd7d47d051054a76937e03482f38e8aacf9cbfc7c8be0b04c144c7789f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:14
Display reorder
35,43,91,39,13,0,1,9,67,99,83,44,36,94,40,88,106,2,68,10,92,14,79,27,65,29,95,15,5,107,7,3,45,28,84,4,30,46,6,16,8,109,66,100,105,73,87,69,11,37,41,53,93,59,89,74,34,60,70,90,42,38,98,54,82,12,21,101,103,17,77,63,85,25,47,31,49,96,22,32,18,50,80,64,48,26,108,78,23,55,51,57,19,97,61,81,71,75,33,56,24,76,58,104,62,102,72,86,52,20,110,115,118,120,119,111,116,112,117,113,114 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 / 8×α=6. • α = 2 on 4 parallel classes (slopes {0, 1, 3, 8}) • α = 6 on 8 parallel classes (slopes {2, 4, 5, 6, 7, 9, 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=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 11:45:53 · history