Equation 677 Database

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Magma 985e14d62209…

magma 985e14d62209
Size
121
Isomorphism class hash
985e14d62209bb98ad27437d2549964de71b46b741b163844319d67972fef3c3
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:26
Display reorder
37,66,67,19,36,120,18,1,62,0,63,110,93,79,32,56,84,8,14,88,2,71,57,80,99,9,117,104,33,3,43,15,89,21,65,4,50,51,85,94,72,111,16,86,52,5,64,100,20,105,49,17,87,44,118,95,39,73,55,6,53,34,30,27,112,78,7,40,38,35,101,106,54,119,77,31,26,60,10,47,22,70,83,114,12,97,92,29,42,48,11,116,61,108,23,103,28,13,98,69,113,90,74,46,109,24,58,96,81,75,45,91,115,25,68,107,41,82,76,59,102 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines carry only TWO line-operation types (in the natural F_11 parameterization x ◇ y = (1-α)x + αy): • 8 parallel classes use α = 6 (the F_11 midpoint quasigroup x ◇ y = 6(x+y) mod 11, which is commutative). • 4 parallel classes use α = 8 (the operation x ◇ y = 4x + 8y mod 11, non-commutative). Globally the magma is NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. The display reorder presents points as (h, v) ∈ F_11 × F_11 where rows/cols of each 11×11 diagonal block correspond to the α=6 'horizontal' parallel class, so all 11 diagonal blocks render as the identical F_11(6,6) Cayley table. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:47 · history