Equation 677 Database

← all  ·  ← by size  ·  ← size 121

Magma aac04c7b85d4…

magma aac04c7b85d4
Size
121
Isomorphism class hash
aac04c7b85d4c8a45953449af4dd8d1d6fb29c68e3212ab01404e90d31250f65
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:23
Display reorder
63,119,1,46,26,99,90,0,30,67,97,2,31,109,64,48,92,27,115,98,100,60,116,94,23,101,66,28,45,32,62,89,3,33,59,16,91,102,47,68,95,4,24,117,96,5,17,25,93,65,103,61,118,44,29,83,57,108,73,85,51,114,15,6,40,36,7,79,106,112,49,71,41,34,11,88,55,12,8,104,42,69,110,86,58,37,52,80,35,13,107,84,113,43,50,81,56,72,9,54,38,105,53,39,87,70,10,82,111,14,74,77,120,18,19,21,20,78,76,22,75 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=7 / 8×α=8. • α = 7 on 4 parallel classes (slopes {0, 1, 5, 9}) • α = 8 on 8 parallel classes (slopes {2, 3, 4, 6, 7, 8, 10, 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=8) 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 11:45:55 · history