Equation 677 Database

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Magma a7088bdc4662…

magma a7088bdc4662
Size
275
Isomorphism class hash
a7088bdc4662f722585c3aa3c952f4fcd3bdcd6b590dfc57af516248e794f56b
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 265 (nullity 10) what is this?
Submitted by
omegaestable
Submitted at
2026-10-07 18:25:24
Display reorder
274,107,106,102,105,99,98,217,208,214,96,210,97,215,218,103,216,213,101,209,104,212,211,219,100,270,249,253,252,255,251,258,272,257,259,260,263,250,266,267,248,269,262,254,265,247,261,256,268,264,220,77,59,64,46,37,36,81,34,35,48,66,57,75,0,67,95,58,49,76,74,47,56,84,65,205,145,166,118,179,137,169,201,159,182,187,135,174,161,199,147,190,151,116,156,129,131,112,196,114,206,168,136,181,158,167,144,191,180,117,111,130,128,113,197,150,194,146,157,115,173,134,188,202,160,207,149,155,125,152,123,186,195,162,175,170,138,183,119,193,143,200,178,110,165,133,127,141,198,122,223,33,12,38,30,18,11,90,24,13,25,50,1,68,92,55,85,10,73,23,60,63,45,87,78,222,41,71,21,53,61,43,94,80,19,31,6,40,28,86,2,89,4,14,16,52,8,70,83,26,221,69,9,51,27,15,5,88,3,17,29,39,7,32,82,79,91,44,62,20,22,72,42,93,54,204,163,176,172,185,184,120,192,171,139,177,108,164,142,203,140,109,121,132,126,154,124,153,189,148,273,232,229,230,226,224,241,245,233,238,225,242,231,239,246,237,244,243,227,240,228,236,234,271,235 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

The table is constructed on \(\mathbb F_{11}\times\mathbb F_5^2\). Its base operation is \(i\circ j=6(i+j)\pmod{11}\). Between different fibers, the fiber output is \(t\) when \(j-i\) is a nonzero square mod 11, and \(-s-t\) otherwise. On the diagonal, fiber 0 uses the order-25 seed \(s*_0t=s+f_1(t-s)\); the other ten fibers use \(2s-t\). The table numbers elements by \(25i+5u+v\) for \((i,(u,v))\), and each entry is the zero-based index of the product. The Paley fiber-product identities give E677; every diagonal seed is idempotent, so the whole table is idempotent and therefore satisfies E255. It is not a counterexample to E677 implying E255.

last edited by omegaestable at 2026-10-07 18:32:45 · history