Equation 677 Database

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Magma 9bf683ab02be…

magma 9bf683ab02be
Size
265
Isomorphism class hash
9bf683ab02be22106f92fc2eb65bb89ae7003de7f121ed6fcdccb5ef9495cd30
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 265 (nullity 0) what is this?
Submitted by
dwrensha
Submitted at
2026-09-04 23:15:05
Display reorder
252,243,255,249,250,240,254,244,260,242,257,245,251,239,253,247,258,241,256,246,259,238,262,248,236,225,231,217,229,223,235,220,263,222,232,218,228,227,233,221,230,226,261,216,237,224,234,219,54,1,68,6,57,48,50,4,213,47,61,13,87,2,75,21,82,29,0,19,89,30,64,11,88,33,77,26,53,34,67,16,215,32,71,24,49,7,60,9,86,8,74,28,81,31,63,18,194,128,182,144,187,121,180,140,198,130,176,139,188,123,155,148,162,132,173,147,159,117,169,143,85,14,73,45,80,3,62,46,212,5,79,38,91,12,66,37,56,20,70,41,59,22,52,42,93,101,94,209,207,205,92,201,264,99,200,96,208,100,97,102,206,203,211,204,202,95,103,98,160,141,170,119,195,142,183,110,196,150,166,109,184,149,177,120,189,146,156,127,163,145,174,126,58,44,51,17,84,35,72,25,214,36,76,15,83,40,78,23,90,39,65,10,55,43,69,27,190,116,164,113,153,129,175,136,199,122,171,137,157,131,181,138,192,124,167,135,185,133,178,114,186,107,179,106,191,112,165,151,197,108,154,152,161,111,172,104,158,118,168,115,193,125,105,134,210 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Simple non-RC Eq677 magma, size 265 = 11*24+1, with NON-NORMAL fiber matrix (F F^T != F^T F) of full rank 265. 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 non-right-cancellative size-25 seed magma#d732efd172ca4d7b9967999fff8c2c19229e25d23884fce7dbc53f3cb456aad4 (e = any of its idempotents; Aut is transitive). Compare magma#dc2f657e34e8de11126c640cda74edb6 (size 275, one non-RC diagonal fiber, non-normal but not simple) and magma#d732efd172ca4d7b9967999fff8c2c19229e25d23884fce7dbc53f3cb456aad4 itself (normal). This is the first known Eq677 magma that is simultaneously simple, non-RC, not translation-invariant and non-normal. 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 23:15:05 · history