Equation 677 Database

Magma d131ee90fbd2…

magma d131ee90fbd2
Size
151
Isomorphism class hash
d131ee90fbd290fd4d4f294cdbf10b59403dde4b2946212b2265bd49a4817deb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:10:24
Display reorder
0,1,135,97,148,138,120,50,89,55,83,15,21,85,129,84,38,149,48,39,46,2,112,95,141,54,117,134,125,81,99,115,63,43,147,127,12,57,136,133,96,119,17,62,86,32,90,143,98,28,77,10,34,114,107,92,5,44,106,49,19,91,42,130,6,26,103,126,101,128,16,41,105,7,66,29,14,131,9,40,67,132,139,24,45,52,18,73,118,65,22,61,87,27,144,71,108,111,82,47,102,122,8,88,140,74,56,100,109,142,79,116,70,137,37,11,4,13,124,3,59,104,60,31,25,58,80,64,75,145,113,123,72,110,36,35,53,51,68,146,23,94,30,150,20,69,33,121,93,76,78 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=92 / 5×δ=143. Per-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:87, coset2:92, coset3:143, coset4:87, coset5:92, coset6:143, coset7:87, coset8:92, coset9:143, coset10:87, coset11:92, coset12:143, coset13:87, coset14:92. 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 12:48:06 · history