Equation 677 Database

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Magma d7e85eadbf36…

magma d7e85eadbf36
Size
121
Isomorphism class hash
d7e85eadbf36415ab80a8afa93504a8062229e3cfdc14cd3e03eb834f1c7fd62
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:01
Display reorder
1,3,54,59,69,96,2,0,119,107,77,41,65,105,49,12,87,44,117,4,103,37,67,22,39,5,51,33,97,27,46,106,118,30,79,17,31,61,71,56,74,6,98,111,45,100,35,88,24,10,66,7,42,85,50,89,8,25,76,34,58,9,101,53,84,68,32,43,64,11,18,48,40,78,110,99,26,28,55,82,81,73,20,13,70,16,115,60,80,38,47,29,83,14,19,52,63,114,15,57,116,23,72,104,75,86,62,36,102,21,94,93,109,95,108,112,113,92,91,120,90 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=7. • α = 6: parallel classes with F_11 slopes {2, 5, 8, INF} • α = 7: parallel classes with F_11 slopes {0, 6, 7, 9} Kept slopes (8): {0, 2, 5, 6, 7, 8, 9, INF}. Removed slopes (4): {1, 3, 4, 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 11:49:13 · history