Equation 677 Database

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Magma 6c5e9b39f87e…

magma 6c5e9b39f87e
Size
121
Isomorphism class hash
6c5e9b39f87eb5593826d732f81ef984d064f4f91f25234fd56e2893490e373b
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-17 12:41:22
Display reorder
80,30,55,110,0,85,107,46,88,2,5,54,91,37,12,73,63,106,103,68,99,1,3,18,95,76,51,31,17,102,62,96,81,71,32,66,4,112,16,8,61,36,52,109,49,28,60,6,15,74,98,44,79,105,108,7,34,77,111,39,45,58,72,114,47,89,35,38,19,9,113,116,53,83,43,78,64,33,90,101,67,82,48,100,97,57,104,10,11,120,13,20,22,26,86,14,25,87,23,119,42,92,50,27,41,84,21,115,69,59,93,40,118,65,56,117,75,94,29,24,70 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Twisted AG(2, 11) magma with exactly 4 of 12 parallel classes preserved (NON-right-cancellative). Size 121 = 11², fully idempotent, NOT right-cancellative. Exactly 44 size-11 sub-magmas in M, partitioning into 4 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; the other 8 parallel classes of AG(2, 11) are NOT closed under the operation. This is the "4-class" sub-family of twisted AG(2, 11) magmas — one of 2 iso classes at size 121 sharing this fingerprint (the other: magma#014291bf). The non-RC property distinguishes it from the "2-class" sub-family (sub-11 = 22, 8 RC iso classes including magma#6bab1ff9) and from the full AG(2, 11) line family (sub-11 = 132, all RC). In the suggested reorder, positions 11·r + c correspond to grid points at the intersection of P1-row r and P2-column c (using 2 of the 4 preserved parallel classes as grid axes). Diagonal 11×11 blocks reveal the row sub-magma operations. See size-121 page commentary for the full taxonomy. [text written by Claude]

last edited by dwrensha at 2026-05-18 17:08:28 · history