Equation 677 Database

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Magma 1c1045d74cc5…

magma 1c1045d74cc5
Size
89
Isomorphism class hash
1c1045d74cc5a6cd35415a2d56a5971c4505b0d3fed33db6316f8fcb706a4e5f
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: yes · rank: 78 (nullity 11) what is this?
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:25:08
Display reorder
0,25,10,75,20,5,30,15,1,26,11,76,21,6,31,16,2,27,12,77,22,7,32,17,3,28,13,78,23,8,33,18,4,29,14,79,24,9,34,19,35,60,45,71,55,40,66,50,36,61,46,72,56,41,65,51,37,63,48,73,58,43,68,53,38,64,49,74,59,44,69,54,39,62,47,70,57,42,67,52,80,86,83,82,85,87,81,84,88 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-89 magma: 88 = 11 × 8 elements form 11 fibers of 8 (with an F_11 base op), plus one adjoined right-identity element e. Left-multiplication by e is a finite-order permutation acting on the fibers. Decoded recipe (2026-09-04, Claude Fable 5.1 with dwrensha; reproduced exactly by construction, server hash matches): carrier {e} + F_11 x Z/8. Base law i*j = 6i + 6j mod 11. Off-diagonal fibers (i != j): (i,s)*(j,t) = (i*j, t) if j-i is a nonzero square mod 11, else (i*j, -s-t mod 8). Each diagonal fiber together with e is a copy of the unique size-9 magma magma#2925dc18 (e = its right identity, the only idempotent), the 11 copies glued along e. For x,y in distinct fibers all four products of Eq677 stay off-diagonal, so the diagonal seeds can be chosen independently; the same recipe with other seeds (any 677 magma with an idempotent, sizes 5, 7, 11, 13, 25) and either idempotent linear base law over F_11 gives further simple non-RC magmas of sizes 11k+1 (45, 67, 89, 111, 133, 265), submitted 2026-09-04. Sibling of this one with base law 10i + 2j: magma#518e9e9a4628157ad68afbac90919217bda484316b89a7fa58f619fea1368b47.

last edited by dwrensha at 2026-09-04 23:14:10 · history