Equation 677 Database

← all  ·  ← by size  ·  ← size 265

Magma 630fd98dfc41…

magma 630fd98dfc41
Size
265
Isomorphism class hash
630fd98dfc410d49c7fdf351f17833f1b9b675a4126577ba433615f5ee778f54
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 255 (nullity 10) what is this?
Submitted by
dwrensha
Submitted at
2026-09-04 23:15:19
Display reorder
97,101,100,209,202,201,92,205,264,96,206,95,208,94,99,102,200,204,211,203,207,98,103,93,257,252,244,246,238,251,243,245,260,256,242,250,259,255,241,249,258,254,240,248,239,253,262,247,1,46,9,68,84,50,13,72,214,54,17,76,91,34,21,56,8,38,25,60,82,42,0,64,190,174,115,152,104,170,134,148,196,166,131,144,184,162,127,140,110,182,123,136,193,178,119,156,194,179,120,157,191,175,116,153,197,171,135,149,108,167,132,145,185,163,128,141,111,183,124,137,107,169,133,147,187,165,130,143,199,161,126,139,109,181,122,159,192,177,118,155,189,173,114,151,88,55,18,77,5,35,22,57,215,39,26,61,83,43,29,65,3,47,10,69,85,51,14,73,81,41,28,63,4,45,31,67,213,49,12,71,87,53,16,75,90,33,20,79,7,37,24,59,6,36,23,58,80,40,27,62,212,44,30,66,2,48,11,70,86,52,15,74,89,32,19,78,112,160,125,138,195,180,121,158,198,176,117,154,188,172,113,150,105,168,106,146,186,164,129,142,236,227,219,233,237,228,220,234,263,223,221,229,216,224,222,230,235,225,261,231,217,226,218,232,210 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Simple non-RC Eq677 magma, size 265 = 11*24+1, with one exceptional diagonal fiber and non-normal fiber matrix (rank 255). 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; fiber 0 uses the non-RC seed magma#d732efd172ca4d7b9967999fff8c2c19229e25d23884fce7dbc53f3cb456aad4 and the other ten fibers use the RC seed magma#011f266679d5012ddc6fb8a93866200462cdbeaadb2c1631b585faedf18b4c26. 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 23:15:19 · history