Equation 677 Database

← all  ·  ← by size  ·  ← size 121

Magma 80bb735bf82b…

magma 80bb735bf82b
Size
121
Isomorphism class hash
80bb735bf82bd5a19caa80aa9af6a8a9ed18a8f1cc3a4e8d7e066bb6e5c25669
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:09
Display reorder
0,120,17,30,33,16,29,34,1,23,22,56,27,83,94,53,18,78,91,2,117,104,3,67,19,46,70,43,99,52,61,81,112,116,65,4,32,74,73,41,55,103,49,93,108,25,89,86,60,5,31,75,111,98,76,97,68,59,6,110,8,71,107,47,15,44,79,28,9,92,109,54,7,115,102,84,14,42,66,39,63,101,114,10,45,36,12,69,35,26,119,11,77,106,58,96,87,90,13,37,24,100,113,51,80,82,85,88,20,62,72,64,48,105,40,95,118,50,38,57,21 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=6 / 4×α=7. • α = 2 on 4 parallel classes (slopes {3, 4, 6, 8}) • α = 6 on 4 parallel classes (slopes {2, 5, 10, INF}) • α = 7 on 4 parallel classes (slopes {0, 1, 7, 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=6) 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 11:45:52 · history