Equation 677 Database

Magma ce9bc37e4e16…

magma ce9bc37e4e16
Size
151
Isomorphism class hash
ce9bc37e4e16a028ca976028a09f3f8129fc33bfc7d98784808cd262d056da25
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:10:30
Display reorder
0,1,140,48,123,113,125,80,26,45,47,15,21,40,144,86,66,114,51,67,74,2,147,30,136,91,102,149,130,29,41,120,42,71,132,112,12,38,131,108,94,134,17,88,79,60,90,118,87,56,43,10,62,129,142,83,5,72,101,52,19,44,70,135,6,54,128,121,146,103,16,69,110,7,99,57,14,126,9,68,28,117,104,24,73,98,18,32,143,35,22,49,33,55,109,39,133,106,93,50,137,107,8,97,145,96,84,105,124,127,36,111,85,122,65,11,4,13,139,3,31,119,95,59,53,77,75,81,25,100,138,148,78,115,64,63,27,34,92,141,23,76,58,150,20,46,61,116,37,89,82 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total). δ-distribution across the 15 cosets: 5×δ=87 / 5×δ=132 / 5×δ=143. Per-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:132, coset2:87, coset3:143, coset4:132, coset5:87, coset6:143, coset7:132, coset8:87, coset9:143, coset10:132, coset11:87, coset12:143, coset13:132, coset14:87. Each δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial. Display reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151). [text written by Claude]

last edited by dwrensha at 2026-05-13 12:48:08 · history