Equation 677 Database

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Magma b62e800066c2…

magma b62e800066c2
Size
121
Isomorphism class hash
b62e800066c2296f62aab257741b2ac079466d77da576d6b621ea73b2403ff7c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:20
Display reorder
120,18,36,19,71,17,1,35,70,0,16,97,66,78,21,56,52,93,82,2,116,104,27,20,63,37,3,45,114,102,86,50,51,29,101,11,62,39,49,85,4,7,14,111,94,81,5,77,6,118,15,106,68,55,92,28,110,8,47,10,38,99,88,24,60,58,98,90,53,117,25,59,79,9,105,75,67,95,43,12,57,119,74,107,69,89,33,83,30,87,40,42,46,64,34,13,112,109,103,26,73,48,44,61,32,22,113,100,41,84,96,108,115,72,76,54,65,91,80,23,31 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): 4×α=6 / 4×α=7 / 4×α=8. • α = 6 on 4 parallel classes (slopes {5, 6, 7, INF}) • α = 7 on 4 parallel classes (slopes {1, 2, 4, 9}) • α = 8 on 4 parallel classes (slopes {0, 3, 8, 10}) 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 11:45:54 · history