Equation 677 Database

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Magma 41b14d976148…

magma 41b14d976148
Size
67
Isomorphism class hash
41b14d9761481fecba35b6847bf8e7ce2d8ebca9cd430bd6d99946d2134f37d8
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: yes · rank: 56 (nullity 11) what is this?
Submitted by
dwrensha
Submitted at
2026-09-04 23:14:47
Display reorder
18,19,20,21,22,23,56,58,59,54,55,57,31,32,33,34,35,30,47,43,44,45,46,42,5,6,7,8,9,10,64,61,60,62,63,65,1,2,3,4,0,11,41,36,38,39,40,37,27,28,29,25,24,26,53,48,50,51,52,49,12,14,15,16,17,13,66 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Simple non-RC Eq677 magma, size 67 = 11*6+1, with two different diagonal seeds. Recipe (see magma#1c1045d74cc5a6cd35415a2d56a5971c for the k=8 prototype): carrier {e} + F_11 x Z/k, 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 k). Each diagonal fiber together with e is a copy of a seed 677 magma of size k+1 with e as an idempotent, all copies glued along e. For x,y in distinct fibers all four products of Eq677 stay off-diagonal, so the seeds can be chosen independently per fiber. Here k=6 and fiber i uses seed magma#7981e2df4cc5c795ad295ab69f55b88db1cecb20c1d1ac4df4d7aa42b92757f1 for even i and seed magma#baf8b55c9a489d3c0ce2405b9167b3a08aada73c1917019843910c3cbab0f48d for odd i (both size-7 magmas with a unique idempotent). Verified locally: Eq677 on all instances, simple (each pair (0,b) generates the full congruence), non-RC, not translation-invariant (e is the unique right identity). Constructed by Claude (Fable 5.1) with dwrensha, 2026-09-04.

last edited by dwrensha at 2026-09-04 23:14:47 · history