Equation 677 Database

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Magma 8b0e368b8f32…

magma 8b0e368b8f32
Size
121
Isomorphism class hash
8b0e368b8f3290fc9aa0bd820f6265e3ae7023c999ea8a783a99388f9dea3fd5
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:06
Display reorder
0,108,47,7,116,1,49,38,81,79,45,52,112,75,54,88,94,35,56,2,12,37,41,31,71,68,110,101,64,3,84,17,24,114,21,67,91,63,10,86,4,58,42,33,26,14,50,76,92,25,61,5,99,105,72,104,77,51,13,73,60,28,98,6,27,93,18,69,70,30,8,65,100,85,36,40,111,43,90,66,22,32,87,9,59,23,115,62,11,55,74,113,16,34,95,15,57,53,89,78,20,46,109,44,48,29,80,39,19,117,118,97,120,96,107,82,83,103,102,119,106 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): 8×α=6. • α = 6: parallel classes with F_11 slopes {0, 1, 3, 4, 5, 8, 10, INF} Kept slopes (8): {0, 1, 3, 4, 5, 8, 10, INF}. Removed slopes (4): {2, 6, 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 11:49:15 · history