Equation 677 Database

Magma 459ccbc5610b…

magma 459ccbc5610b
Size
151
Isomorphism class hash
459ccbc5610b41cb9c641b20654c23863b85242e74902239ae3f6a70fc0c27e0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:10:59
Display reorder
0,1,39,58,127,137,135,108,61,55,57,15,21,50,30,114,86,35,96,87,94,2,148,65,48,119,37,131,49,64,51,34,52,91,32,27,12,73,134,36,122,40,17,116,107,80,118,26,115,76,53,10,82,126,47,111,5,92,139,97,19,54,90,125,6,99,41,144,38,147,16,89,44,7,102,77,14,33,9,88,63,128,45,24,93,101,18,67,132,70,22,59,68,75,146,74,142,28,121,95,133,138,8,100,140,124,112,130,25,143,71,129,113,42,85,11,4,13,141,3,66,136,123,79,98,105,103,109,60,29,31,46,106,145,84,83,62,69,120,149,23,104,78,150,20,56,81,43,72,117,110 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=132 / 10×δ=143. Per-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:132, coset2:143, coset3:143, coset4:132, coset5:143, coset6:143, coset7:132, coset8:143, coset9:143, coset10:132, coset11:143, coset12:143, coset13:132, coset14:143. 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 12:48:17 · history