Equation 677 Database

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Magma e728039473d8…

magma e728039473d8
Size
121
Isomorphism class hash
e728039473d8281487717462e92cda34e4044cdc5512902c689f976a56d2229d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:53
Display reorder
38,75,102,44,115,59,0,27,30,1,68,97,80,33,64,29,49,28,2,110,67,106,47,78,62,5,20,118,3,104,24,41,95,57,73,52,113,23,6,65,4,19,100,36,7,79,9,105,96,16,48,63,42,119,26,10,74,8,15,37,66,58,43,101,25,114,14,81,111,17,107,11,98,34,54,50,55,116,76,13,12,53,18,39,93,109,60,45,108,82,71,35,56,99,21,112,51,32,70,72,77,103,94,46,40,117,22,61,69,31,83,120,88,90,92,85,84,89,87,86,91 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): 8×α=2 / 4×α=6. • α = 2 on 8 parallel classes (slopes {0, 1, 2, 4, 5, 7, 8, 10}) • α = 6 on 4 parallel classes (slopes {3, 6, 9, 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 11:45:51 · history