Equation 677 Database

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Magma c8dcedeb66e0…

magma c8dcedeb66e0
Size
121
Isomorphism class hash
c8dcedeb66e0d3938358cbc800c5c87189642160f1774fe6ecdb0d569e7825ef
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:55
Display reorder
37,3,65,0,103,39,109,91,72,8,54,108,77,1,60,43,102,36,7,29,90,49,2,9,44,82,92,32,105,34,61,68,50,104,66,83,38,33,93,19,73,10,4,55,35,45,99,17,21,111,69,62,95,5,51,74,94,18,98,110,20,22,6,40,67,56,26,23,112,30,75,11,58,41,88,96,57,63,89,31,113,12,70,25,97,24,46,52,42,87,76,16,116,59,106,114,27,13,48,107,28,15,71,64,117,47,14,86,115,53,78,100,81,80,84,85,79,119,101,118,120 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=2 / 4×α=6. • α = 2: parallel classes with F_11 slopes {0, 1, 3, 7} • α = 6: parallel classes with F_11 slopes {4, 5, 10, INF} Kept slopes (8): {0, 1, 3, 4, 5, 7, 10, INF}. Removed slopes (4): {2, 6, 8, 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 11:49:07 · history