Equation 677 Database

Magma 644c60e3104b…

magma 644c60e3104b
Size
151
Isomorphism class hash
644c60e3104bb9b63985595a7b7e60e0694e1d289303945ed868366e298562e0
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:10:55
Display reorder
0,1,149,113,56,52,93,75,109,146,61,144,119,49,17,13,11,145,16,86,85,64,42,35,108,124,76,134,103,67,147,100,73,27,30,118,62,88,101,6,116,45,150,15,66,36,51,138,112,68,25,22,123,148,97,117,53,84,126,74,58,5,12,114,135,136,46,95,41,43,47,19,69,94,111,96,59,125,143,102,106,63,98,31,99,139,14,130,121,127,72,55,24,120,92,39,104,107,128,26,90,20,33,65,79,60,10,28,81,38,18,82,34,133,7,32,87,141,91,137,2,37,83,4,132,48,8,131,23,40,110,129,115,3,50,140,21,78,57,54,9,142,70,29,105,122,77,71,80,44,89 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 = 129 (count 50, order 150 in F_151*, NOT in H) • ratio δ(d)/d = 92 (count 50, order 10 in F_151*, IN H) • ratio δ(d)/d = 145 (count 50, order 75 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 12:49:43 · history