Magma 086278678c74 — Equation 677 Database

Magma `086278678c74…`

Size: 111
Isomorphism class hash: 086278678c749318ef81e8439e3a38e7e886b35394fc54a7a129e30e7a76ccb7
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 23:14:54
Display reorder: 85,68,78,66,55,53,72,74,62,48,82,56,50,73,75,63,49,58,69,79,106,101,100,98,103,105,102,108,99,104,109,96,91,107,94,97,95,90,92,93,86,33,23,12,3,17,29,27,4,10,89,2,16,28,26,7,9,20,32,22,84,76,64,47,59,70,80,60,57,51,87,19,31,21,6,8,15,35,25,1,110,40,43,45,41,38,42,36,37,39,83,46,71,81,61,54,52,67,77,65,88,5,11,14,34,24,13,0,18,30,44 history
Raw table: canonical order · displayed order
Equational Theories: Finite Magma Explorer

Simple non-RC Eq677 magma, size 111 = 11*10+1, mixing all four idempotent size-11 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=10 and fiber i uses seed number (i mod 4) from the list magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39, magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc, magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc, magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 23:14:54 · history