Equation 677 Database

← all  ·  ← by size  ·  ← size 121

Magma ce5d89d56c90…

magma ce5d89d56c90
Size
121
Isomorphism class hash
ce5d89d56c9069c6008cb2e1d6d3a96f65c626e1528fda77c4c5dc9ec8e50791
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:45
Display reorder
104,108,107,120,109,2,3,106,1,0,105,110,50,26,93,64,32,10,87,99,4,47,53,27,85,91,5,102,33,48,65,13,113,28,88,44,89,11,66,100,111,6,29,51,86,45,114,92,30,7,67,49,9,103,24,46,112,52,90,101,12,8,25,31,68,84,42,19,72,78,61,14,115,96,56,36,81,69,97,83,74,116,62,58,43,38,15,21,80,39,23,75,55,117,35,71,16,63,98,20,73,94,76,37,57,17,82,59,118,40,95,79,41,77,18,34,60,22,119,54,70 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=7 / 6×α=8. • α = 7 on 6 parallel classes (slopes {1, 2, 3, 5, 10, INF}) • α = 8 on 6 parallel classes (slopes {0, 4, 6, 7, 8, 9}) 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 11:45:58 · history