Equation 677 Database

← all  ·  ← by size  ·  ← size 121

Magma fdc3bc3fe5e6…

magma fdc3bc3fe5e6
Size
121
Isomorphism class hash
fdc3bc3fe5e609f46272fb80974e4cfce83a35a9a8d17cb71cd232542ddc7c59
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:57
Display reorder
80,29,1,109,0,24,45,107,48,96,54,95,101,23,93,47,36,104,33,56,50,2,78,89,44,52,113,18,9,17,3,53,84,91,57,27,4,21,119,11,43,110,98,51,81,5,30,34,108,70,97,58,106,64,25,114,49,87,55,12,46,6,15,103,117,82,115,86,59,13,71,83,116,102,8,7,65,90,28,68,20,31,61,99,111,67,10,118,79,63,88,112,62,85,69,14,16,26,19,94,22,100,66,92,35,60,72,32,105,37,120,39,75,41,73,77,76,74,42,38,40 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-121 non-right-cancellative idempotent magma built on the point set of the affine plane AG(2, 11), but with only 8 out of 12 parallel classes of lines preserved by the operation. These 88 'kept' lines are exactly the size-11 sub-quasigroups of the magma; pairs lying on a 'removed' line (slopes in F_11 P¹ where the line is NOT a sub-quasigroup) instead generate the whole magma under the closure of ◇. Per-class α (in F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=6 / 4×α=8. • α = 6: parallel classes with F_11 slopes {4, 6, 8, INF} • α = 8: parallel classes with F_11 slopes {0, 3, 5, 10} Kept slopes (8): {0, 3, 4, 5, 6, 8, 10, INF}. Removed slopes (4): {1, 2, 7, 9}. Each column of the Cayley table is non-injective (collapse fibers), hence the magma is non-right-cancellative; nevertheless it is left-cancellative and every element is idempotent. 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. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:49:09 · history