Equation 677 Database

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Magma 90626b88af6c…

magma 90626b88af6c
Size
121
Isomorphism class hash
90626b88af6c2533483bee5758fe19d239b8b14a69995f3f111e70807bee1be7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:50
Display reorder
107,22,109,106,108,1,105,103,0,104,120,15,114,27,84,77,42,36,19,2,99,69,112,38,97,75,3,20,16,37,25,92,70,39,21,90,4,23,33,110,12,95,73,71,17,34,81,31,93,13,40,118,88,5,72,35,14,6,101,86,116,18,41,79,29,68,61,24,7,111,64,96,74,91,54,50,47,32,94,51,65,55,89,62,82,8,119,43,102,87,117,56,9,80,30,58,52,66,44,85,78,67,10,48,59,100,28,115,57,45,76,60,53,49,113,26,83,98,63,11,46 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=7. • α = 2 on 6 parallel classes (slopes {1, 3, 4, 5, 7, INF}) • α = 7 on 6 parallel classes (slopes {0, 2, 6, 8, 9, 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=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 11:45:59 · history