Equation 677 Database

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Magma 6fec6f96bcd0…

magma 6fec6f96bcd0
Size
121
Isomorphism class hash
6fec6f96bcd08257200e24bf65029d536066debcfd3c186f35cf51e44e6f4c79
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:42
Display reorder
28,0,1,29,120,80,41,32,33,81,40,36,85,50,27,2,109,116,88,23,75,44,26,49,101,37,3,59,55,22,94,107,114,73,47,119,78,57,91,4,83,21,42,34,105,112,53,62,56,43,35,20,99,97,5,64,8,69,89,14,86,71,45,117,6,76,95,70,9,63,15,7,108,110,51,102,60,52,31,96,111,39,17,103,61,104,19,10,118,90,30,46,38,18,11,77,72,16,82,68,79,74,84,25,48,93,65,12,115,87,100,58,106,67,24,113,98,13,66,54,92 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=6 / 6×α=8. • α = 6 on 6 parallel classes (slopes {3, 4, 5, 6, 10, INF}) • α = 8 on 6 parallel classes (slopes {0, 1, 2, 7, 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=8) operation. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:57 · history