Equation 677 Database

Magma 18ebb6890d34…

magma 18ebb6890d34
Size
151
Isomorphism class hash
18ebb6890d340ba51ebafe8b15d861c7fc126833335b5435067ee5064a1d6ea1
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:11:07
Display reorder
0,1,146,125,65,144,35,127,73,14,121,104,40,4,114,48,53,36,66,5,120,138,131,105,20,60,58,87,118,128,9,134,119,72,142,133,147,97,83,92,122,69,84,34,78,68,137,108,110,45,55,81,88,70,30,116,11,103,23,64,29,15,54,71,39,123,77,10,94,115,75,96,26,99,22,24,79,141,135,27,67,28,145,74,132,149,56,111,136,7,51,18,102,130,46,38,12,33,89,113,93,50,59,62,148,41,19,6,107,76,42,90,150,140,17,126,57,31,44,16,100,112,109,25,143,63,139,8,37,13,21,80,52,43,101,32,86,61,106,98,82,124,95,3,117,2,85,91,129,49,47 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 50, order 10 in F_151*, IN H) • ratio δ(d)/d = 92 (count 50, 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 12:49:46 · history