Equation 677 Database

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Magma e5ec2793fb38…

magma e5ec2793fb38
Size
121
Isomorphism class hash
e5ec2793fb38d2870818a449abc1611b93d9832248e8f38cc260d4b1bf8df614
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:17
Display reorder
120,11,40,39,7,10,77,1,6,78,0,60,82,110,4,45,88,69,2,106,22,72,101,58,5,117,20,48,21,89,98,34,3,100,97,8,33,116,29,17,47,19,93,57,64,105,68,9,18,44,76,87,114,16,81,103,66,55,50,91,31,95,119,53,27,12,62,71,79,85,54,65,108,13,74,42,112,99,52,35,92,32,115,56,28,14,46,96,63,113,75,36,15,51,80,43,67,86,104,61,73,107,41,84,23,111,38,83,25,70,102,24,94,109,49,90,26,30,59,118,37 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 / 8×α=8. • α = 6 on 4 parallel classes (slopes {1, 5, 9, INF}) • α = 8 on 8 parallel classes (slopes {0, 2, 3, 4, 6, 7, 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 11:45:53 · history