Equation 677 Database

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Magma 1e5dad274948…

magma 1e5dad274948
Size
265
Isomorphism class hash
1e5dad27494889526feb5b844e5efdfb7718d126af0a1112fb2ec970523de751
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: yes · rank: 254 (nullity 11) what is this?
Submitted by
dwrensha
Submitted at
2026-09-04 23:15:09
Display reorder
252,242,262,247,245,257,250,240,260,253,243,255,248,246,258,251,241,256,254,244,238,249,239,259,219,229,236,224,226,233,221,231,263,218,228,235,223,225,261,220,230,237,217,227,216,222,232,234,8,46,1,28,66,80,16,54,214,3,42,71,24,62,76,12,50,82,32,38,68,20,58,89,27,65,79,15,53,85,35,41,215,23,61,75,11,49,81,31,37,74,19,57,88,7,45,2,179,141,188,159,120,202,171,133,208,183,145,117,163,125,206,175,137,185,155,149,199,167,129,193,34,40,70,22,60,91,10,48,213,30,36,6,18,56,87,5,44,73,26,64,78,14,52,84,110,98,106,97,93,96,111,113,264,104,103,109,94,112,115,105,92,100,107,101,95,108,99,102,160,121,203,172,134,122,152,146,209,164,126,207,176,138,186,156,150,200,168,130,194,180,142,189,21,59,90,9,47,0,29,67,212,17,55,86,4,43,72,25,63,77,13,51,83,33,39,69,153,147,197,165,127,191,177,139,211,157,151,201,169,131,195,181,143,118,161,123,204,173,135,190,166,128,192,178,140,187,158,119,210,170,132,196,182,144,116,162,124,205,174,136,184,154,148,198,114 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Simple non-RC Eq677 magma, size 265 = 11*24+1. 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=24 and every diagonal fiber uses the right-cancellative idempotent size-25 seed magma#011f266679d5012ddc6fb8a93866200462cdbeaadb2c1631b585faedf18b4c26. Fiber matrix normal, rank 254. 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 23:15:10 · history