Equation 677 Database

Magma 873c2695e304…

magma 873c2695e304
Size
121
Isomorphism class hash
873c2695e304ab27228f4348549fa7ab1dbf7f32d69d7f936466a2114b459a1d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-17 12:41:46
Display reorder
0,2,43,7,26,67,49,79,95,48,69,1,82,9,23,101,11,70,54,40,55,72,103,18,102,78,115,53,30,113,74,105,80,96,47,71,97,75,33,111,21,106,119,77,118,108,84,65,99,116,27,39,100,50,86,20,45,10,92,37,85,5,46,3,73,60,68,36,112,90,91,117,110,56,87,24,89,22,38,19,25,28,35,32,41,16,44,120,31,64,104,6,13,58,57,8,29,76,66,81,107,94,109,62,15,59,114,93,42,83,98,52,17,34,12,51,88,61,4,14,63 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-121 RC idempotent magma on F_121 = F_11² with NO size-11 sub-magmas — an "order-8 multiplier" construction outside the standard Phi_10 family. Size 121, fully idempotent, right-cancellative. Sub-magma count by size: only 0 (singletons) and 121 (the whole magma). Every pair of distinct points generates the entire 121-element magma — there are NO non-trivial sub-magmas. L_0 and R_0 each have cycle structure **1 + 15·8** — the multiplier in the F_121 linear operation has order **8**, not 10. This places the magma outside Pace Nielsen's standard Type-1 (Phi_10 roots, multiplier order 10) and Type-2 (Phi_2_5 roots) classification. Instead, the construction uses an element of the order-8 subgroup of F_121* = (F_121*)^15. The additive structure is F_11² (= F_121 additively). In the suggested reorder, two commuting order-11 fix-free automorphisms t1, t2 of M are chosen as grid generators; position 11·a + b corresponds to the point t1^a(t2^b(0)). The resulting Cayley table shows a clean 11×11 grid of 11×11 sub-blocks, each block showing diagonal-stripe structure characteristic of the F_11² translation action. Family at size 121 sharing this fingerprint (1 + 15·8 cycle): 5 RC idempotent iso classes — magma#70e5572a, magma#58669675, magma#af70b7bb, magma#fdc7e335. They likely correspond to different (α, β) choices among the F_121 multipliers of order 8, modulo Galois conjugacy. This is one of the "sub-11 = 0" magmas distinct from the F_121 affine line (Phi_10 multiplier, would have sub-11 = 132 if used) and the Zassenhaus near-field (magma#5ebfbb80, multiplier order 30). [text written by Claude]

last edited by dwrensha at 2026-05-18 17:20:07 · history