Equation 677 Database

Magma 25f178bfb833…

magma 25f178bfb833
Size
151
Isomorphism class hash
25f178bfb833e40b92923cd0968b304569de2ed66e33be7f8277c71ac459c7f6
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:10:44
Display reorder
0,1,59,146,77,48,116,33,44,41,2,129,74,108,82,134,101,142,68,65,132,71,28,114,144,12,72,103,100,75,136,17,89,85,47,76,110,83,38,52,20,39,131,124,84,15,49,123,29,9,58,32,147,11,46,120,143,118,145,21,36,122,7,80,34,4,148,24,40,62,149,106,14,45,99,13,61,135,54,22,63,67,42,111,53,125,128,94,37,119,139,3,93,107,87,90,117,126,109,60,133,96,104,27,16,19,8,141,23,55,121,81,26,25,98,86,97,69,112,130,140,79,127,31,35,56,73,88,113,18,92,30,150,5,70,43,138,66,95,78,10,6,102,57,115,105,137,91,50,64,51 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 / 5×δ=132 / 5×δ=143. Per-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:143, coset2:92, coset3:132, coset4:143, coset5:92, coset6:132, coset7:143, coset8:92, coset9:132, coset10:143, coset11:92, coset12:132, coset13:143, 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 12:48:13 · history