Equation 677 Database

← all  ·  ← by size  ·  ← size 121

Magma 6cced9128206…

magma 6cced9128206
Size
121
Isomorphism class hash
6cced9128206e81c8a24efc12ee2c4f73c4bc93856f33dc61a29ae4f8583f983
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:44
Display reorder
120,39,40,2,3,1,42,4,41,0,38,71,24,5,116,93,11,18,59,80,89,63,56,77,117,48,17,81,36,6,94,44,31,68,20,65,8,91,95,7,118,26,61,82,69,78,21,62,9,114,27,92,66,101,107,70,103,84,97,58,88,67,10,22,110,23,72,64,25,90,112,60,86,99,105,12,19,57,32,73,45,49,106,100,13,113,87,37,53,33,28,83,46,14,119,50,74,109,96,54,102,34,108,79,51,75,47,29,15,115,55,111,98,16,104,43,30,85,35,52,76 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 / 8×α=8. • α = 2 on 4 parallel classes (slopes {0, 5, 7, 8}) • α = 8 on 8 parallel classes (slopes {1, 2, 3, 4, 6, 9, 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=2) operation. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:49 · history