Equation 677 Database

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Magma 33f36e4e3544…

magma 33f36e4e3544
Size
279
Isomorphism class hash
33f36e4e354485aa6d83c3495c0805bbe1148f10127d869f88de86140bddb8eb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
omegaestable
Submitted at
2026-07-22 03:42:08
Display reorder
271,244,2,1,36,17,32,34,213,276,55,58,59,57,60,22,218,56,250,90,27,223,87,88,85,86,89,255,228,116,115,120,117,118,119,16,260,145,148,149,233,150,147,11,146,265,179,177,6,176,238,180,175,178,270,212,210,206,209,205,243,208,207,275,50,51,52,217,53,49,21,54,248,83,79,26,80,222,84,81,82,254,31,114,110,113,109,227,112,111,259,140,232,142,12,143,139,141,144,264,172,170,171,169,7,173,174,237,269,201,203,204,202,200,211,242,199,274,47,216,48,20,45,44,43,46,249,75,74,73,78,25,76,77,221,253,105,107,108,106,104,30,226,103,258,138,13,231,135,136,134,133,137,263,236,163,164,168,165,166,167,8,268,193,196,197,241,198,195,247,194,273,41,19,215,38,246,42,39,40,278,220,72,68,71,67,69,70,24,252,97,100,101,225,102,99,29,98,257,131,129,14,127,230,132,128,130,262,9,162,158,161,157,235,160,159,267,187,240,190,4,191,188,189,192,272,33,0,18,3,214,35,37,245,277,23,65,66,64,62,219,63,61,251,92,224,94,28,95,91,93,96,256,124,121,123,122,15,125,126,229,261,153,155,156,154,152,10,234,151,266,186,5,239,183,184,181,182,185 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

279-element magma on F_31 x F_3^2 # Operation: (x,(r0,r1)) * (y,(s0,s1)) = (5*x + 27*y + 1 mod 31, A*(s0,s1)^T + (r0,r1)^T mod 3) # A = [[0,1],[1,1]], H = I_2 # Element index: idx(x,(u,v)) = 9*x + 3*u + v (0-based) # Inverse decoding: x = idx // 9; u = (idx % 9) // 3; v = idx % 3 # Matrix check p: A(AHA+H)=I -> True # Matrix check q: A^3+A^2 H^2+H=0 -> True

last edited by omegaestable at 2026-07-22 03:42:44 · history