Equation 677 Database

Magma 94e87e20bb87…

magma 94e87e20bb87
Size
151
Isomorphism class hash
94e87e20bb87109b08412f42b75a866a5d54bb9c021a9d88f5102d66726b15ed
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:10:50
Display reorder
0,1,32,102,65,50,73,135,114,140,148,15,21,120,48,109,84,28,94,85,92,2,61,130,41,129,30,69,42,126,124,27,128,89,25,45,12,112,72,29,141,33,17,117,131,78,125,44,113,99,132,10,80,64,40,147,5,90,52,95,19,136,88,63,6,97,34,57,31,60,16,87,37,7,111,75,14,26,9,86,122,66,38,24,91,107,18,138,70,100,22,106,142,98,59,116,55,46,137,93,71,51,8,103,53,149,101,68,43,56,104,67,105,35,83,11,4,13,54,3,134,74,145,77,96,123,115,139,110,47,49,39,127,58,82,81,118,146,133,62,23,119,76,150,20,144,79,36,108,121,143 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=92 / 10×δ=143. Per-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:92, coset2:143, coset3:143, coset4:92, coset5:143, coset6:143, coset7:92, coset8:143, coset9:143, coset10:92, coset11:143, coset12:143, coset13:92, 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 12:48:15 · history