Equation 677 Database

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Magma 61c16114c7b2…

magma 61c16114c7b2
Size
121
Isomorphism class hash
61c16114c7b2423f3ff97def48877e88f993e5cb313f2d85864755a8bd784b92
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:28
Display reorder
1,80,44,70,0,23,111,87,50,96,45,92,24,101,46,116,75,2,106,49,43,69,17,5,56,65,94,119,28,78,8,3,85,73,114,4,90,27,6,99,18,7,55,104,64,108,68,93,48,84,77,9,31,118,57,10,89,113,58,82,103,47,63,32,67,98,117,102,107,11,29,54,22,59,62,83,76,60,53,88,81,21,97,30,112,61,109,12,95,51,79,72,66,16,86,13,19,26,110,14,15,25,115,91,52,105,100,20,74,71,33,40,39,41,42,35,37,38,120,34,36 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=6. • α = 2 on 6 parallel classes (slopes {0, 1, 4, 5, 7, 9}) • α = 6 on 6 parallel classes (slopes {2, 3, 6, 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=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 11:45:55 · history