Equation 677 Database

Magma 3528ae88c6aa…

magma 3528ae88c6aa
Size
151
Isomorphism class hash
3528ae88c6aa0234425d74b1bda84ea875a7e11fa0c1d6187f1353c039865213
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:11:02
Display reorder
0,1,45,62,111,96,116,92,105,127,95,139,11,25,135,54,137,8,114,48,2,10,39,149,115,70,97,138,144,82,143,107,102,79,28,78,118,29,91,80,126,113,74,49,81,133,44,125,106,109,18,51,41,32,84,58,121,21,22,140,42,37,123,34,72,15,30,86,100,148,136,5,40,122,9,73,12,17,90,47,46,71,108,134,7,16,101,43,59,56,75,19,83,131,24,124,63,76,130,141,4,68,128,3,129,52,57,93,132,94,88,147,120,65,98,14,35,27,23,64,33,87,104,85,50,36,89,145,77,55,142,66,146,61,112,20,26,99,103,69,60,13,117,6,150,31,67,38,110,119,53 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative. Per-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively): • ratio δ(d)/d = 87 (count 100, order 10 in F_151*, IN H) • ratio δ(d)/d = 94 (count 50, order 25 in F_151*, NOT in H) Compared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots. Display reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151). [text written by Claude]

last edited by dwrensha at 2026-05-13 12:49:45 · history