Equation 677 Database

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Magma a9903b15faf8…

magma a9903b15faf8
Size
111
Isomorphism class hash
a9903b15faf869c1c9ff854970e5cba0ce68d862dd6a5b91df98ac5c686117ce
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: yes · rank: 100 (nullity 11) what is this?
Submitted by
dwrensha
Submitted at
2026-09-04 23:14:56
Display reorder
110,40,43,45,41,38,42,36,37,39,106,101,100,98,103,105,102,108,99,104,87,19,31,21,0,8,15,35,25,1,82,52,49,73,75,63,56,58,69,79,84,76,64,57,59,70,80,60,53,50,85,68,78,66,51,48,72,74,62,55,89,9,16,28,26,2,5,20,32,22,88,4,7,14,34,24,13,11,18,30,86,33,23,12,10,17,29,27,3,6,83,46,71,81,61,54,47,67,77,65,109,96,91,107,94,97,95,90,92,93,44 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Simple non-RC Eq677 magma, size 111 = 11*10+1, with one exceptional diagonal fiber. 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=10; fiber 0 uses seed magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39 and the other ten fibers use seed magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 23:14:56 · history