Equation 677 Database

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Magma 014291bf5910…

magma 014291bf5910
Size
121
Isomorphism class hash
014291bf591068236bbc4abf57aa75c6a93c8beb6e63f68352f53280cbad0e14
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:24:59
Display reorder
34,75,71,35,107,0,74,76,70,106,1,4,99,53,5,13,3,98,112,52,12,2,61,96,62,60,16,6,97,113,63,17,7,33,45,72,32,104,8,44,77,73,105,9,59,69,41,58,10,94,68,110,40,11,95,54,15,83,55,116,19,14,108,82,117,18,84,64,20,85,30,47,65,119,21,31,46,87,25,38,86,36,23,24,118,39,37,22,26,66,29,27,51,93,67,111,28,50,92,56,48,80,57,114,42,49,109,81,115,43,102,88,79,103,101,90,89,120,78,100,91 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 4 out of 12 parallel classes of lines preserved by the operation. These 44 '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. • α = 6: parallel classes with F_11 slopes {0, 4, 7, INF} Kept slopes (4): {0, 4, 7, INF}. Removed slopes (8): {1, 2, 3, 5, 6, 8, 9, 10}. 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 11:49:11 · history