Equation 677 Database

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Magma d0e8100118d7…

magma d0e8100118d7
Size
121
Isomorphism class hash
d0e8100118d7fb2c967447ff2e847afb81b4518e117af6fbf16d121199607a0b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:47
Display reorder
30,120,4,0,29,1,31,28,32,3,2,95,58,5,116,44,39,50,71,91,107,65,47,61,105,42,72,6,93,89,51,63,114,68,59,66,7,87,103,45,52,101,112,40,85,62,110,17,48,64,69,99,43,38,8,49,60,41,67,97,118,83,46,70,9,15,115,76,90,27,21,53,78,34,106,10,94,19,74,11,54,35,88,113,104,81,102,25,36,77,100,86,109,12,22,79,111,23,55,16,75,26,13,82,98,37,119,20,56,84,80,73,57,96,117,24,108,18,33,92,14 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=2 / 4×α=7 / 4×α=8. • α = 2 on 4 parallel classes (slopes {1, 3, 8, 9}) • α = 7 on 4 parallel classes (slopes {2, 4, 6, INF}) • α = 8 on 4 parallel classes (slopes {0, 5, 7, 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=7) 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 11:45:49 · history