Equation 677 Database

Magma 89ce585f4851…

magma 89ce585f4851
Size
151
Isomorphism class hash
89ce585f4851edbba74ee862aed5914477d4af552a8cdf78c19a94aa37f95027
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:10:39
Display reorder
0,1,65,149,54,49,119,34,45,42,2,132,75,111,74,137,104,145,71,69,135,73,29,117,147,12,57,106,103,86,139,17,62,76,48,70,113,58,39,77,20,40,134,127,92,15,25,126,30,9,81,33,100,11,47,123,146,121,148,21,37,125,7,56,35,4,101,24,41,67,102,109,14,46,52,13,83,138,95,22,51,87,43,114,61,128,131,82,38,122,142,3,98,110,94,96,120,129,112,99,136,50,107,28,16,19,8,144,23,79,124,90,27,26,68,60,84,55,115,133,143,72,130,32,36,63,91,78,116,18,64,31,150,5,89,44,141,53,66,88,10,6,105,97,118,108,140,80,59,85,93 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: 10×δ=92 / 5×δ=132. Per-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:92, coset2:92, coset3:132, coset4:92, coset5:92, coset6:132, coset7:92, coset8:92, coset9:132, coset10:92, coset11:92, coset12:132, coset13:92, 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 12:48:11 · history