Equation 677 Database

← all  ·  ← by size  ·  ← size 817

Magma a86cf4c37cde…

magma a86cf4c37cde
Size
817
Isomorphism class hash
a86cf4c37cdefbf08e13e0f1a6d9c90d533512954d9abe411a77734f19924331
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 816) what is this?
Submitted by
dwrensha
Submitted at
2026-09-27 18:53:07
Display reorder
812,639,10,729,677,143,454,311,487,786,366,700,592,465,147,54,626,319,530,263,387,41,216,623,350,247,239,208,255,618,457,358,303,669,631,149,328,224,461,360,7,198,587,395,472,734,271,552,393,538,394,195,327,658,617,634,215,272,53,27,486,155,638,220,473,550,498,600,205,322,708,588,118,374,400,719,794,423,8,495,641,170,193,689,532,462,645,556,151,771,93,685,329,436,737,452,324,18,801,632,647,57,293,694,696,96,304,682,258,165,100,122,364,458,713,576,25,5,344,377,256,482,703,516,420,277,106,240,129,145,347,67,521,218,351,22,477,362,161,283,284,217,507,105,60,376,528,363,388,95,598,800,290,684,23,531,83,422,535,707,775,219,627,214,565,537,183,586,68,148,782,254,603,40,234,146,593,310,788,811,237,411,241,367,717,174,397,49,418,278,488,180,38,765,425,665,517,455,739,750,672,493,124,483,678,127,131,607,287,308,378,11,315,407,629,562,806,1,813,177,268,79,519,570,577,158,409,467,299,189,816,459,569,71,805,554,307,300,123,475,664,447,417,172,410,166,233,803,585,32,774,578,683,211,527,523,282,87,520,97,276,354,343,185,121,269,695,369,17,450,92,674,814,58,793,444,321,763,637,807,633,415,392,580,197,542,630,19,207,650,386,544,464,316,453,141,295,610,231,615,379,437,139,692,479,135,44,288,686,404,202,491,784,759,132,772,51,501,111,613,680,679,557,758,81,43,747,614,125,463,743,541,525,636,502,673,690,120,433,86,652,773,740,171,46,306,443,188,760,518,496,561,654,286,574,492,426,424,563,48,251,236,405,39,720,182,341,706,725,289,489,375,547,160,249,66,136,419,589,4,245,99,29,693,398,323,796,770,514,192,438,718,601,204,102,154,77,616,242,551,90,6,62,668,611,238,221,262,723,591,790,142,789,156,667,338,76,791,317,594,28,756,191,620,724,545,235,273,573,754,187,222,651,604,635,643,746,227,612,20,783,659,134,715,230,63,543,69,196,430,762,390,91,581,184,539,281,333,31,243,416,566,553,752,298,732,78,808,628,735,606,73,671,103,764,776,396,36,810,371,602,445,536,199,534,384,799,439,59,84,361,113,346,512,515,675,24,225,164,656,292,797,451,291,150,511,169,798,399,370,599,670,485,731,657,30,270,389,359,229,302,226,246,186,529,619,699,75,676,590,355,61,209,153,14,513,137,98,508,248,559,705,114,250,88,285,624,442,428,85,548,524,162,42,711,110,440,490,212,478,264,609,313,385,726,579,352,320,661,449,200,342,33,522,55,584,778,446,721,804,348,466,331,267,372,406,167,130,701,749,108,37,252,173,107,787,266,253,777,564,448,421,312,597,109,104,427,476,704,144,13,702,74,575,301,257,730,65,168,736,655,555,345,640,383,373,809,497,72,26,297,326,332,733,761,460,714,357,745,349,753,318,190,365,337,728,722,567,47,468,101,413,769,779,244,741,159,259,340,2,56,334,653,571,305,470,432,34,540,434,80,697,500,505,201,582,691,178,294,381,649,662,391,503,815,648,16,504,353,431,526,0,802,768,663,727,70,744,408,325,176,382,314,64,126,12,738,596,179,265,716,748,309,330,781,583,213,660,82,608,94,710,506,441,21,558,128,152,481,698,712,228,681,484,646,510,435,163,644,112,494,533,117,35,549,605,52,751,194,280,471,429,223,133,456,642,622,572,625,755,785,666,9,261,335,89,274,203,766,795,402,3,115,546,687,181,401,688,260,560,621,45,279,119,116,742,509,757,480,50,709,403,780,138,595,140,175,206,767,414,15,792,380,368,499,275,469,210,339,232,412,474,336,568,356,157,296 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Monogenic cyclic-affine Eq677 magma of order 817. On Z/817, in construction labels, x*y = 178x + 402y + 1 (mod 817). Element 0 generates the whole magma; there are 756 generators and 1 idempotent element(s). For any element r, the generated submagma has size 817/gcd(817, (178+402-1)r+1). Both coefficients are units modulo 817, so this is a quasigroup (left- and right-cancellative); its fiber matrix is all ones. The affine Eq677 conditions are ab(1+b^2)=1, a+a^2*b^2+b^3=0, and (b^2(a+1)+b+1)c=0 modulo n. These hold for the displayed parameters. Independently checked all 667489 Eq677 instances, all 817 Eq255 instances, and full set closure from generator 0 directly in the saved table. This is not a counterexample to Eq677 => Eq255. Found while enumerating monogenic cyclic-affine models of orders below 1000, working upward in order. These are standard affine constructions, added to fill gaps in the database. Construction labels may differ from the server canonical labels. Computed with OpenAI Codex working with dwrensha, 2026-09-27.

last edited by dwrensha at 2026-09-27 18:53:07 · history