Equation 677 Database

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Magma ca169959bf18…

magma ca169959bf18
Size
871
Isomorphism class hash
ca169959bf1896e0208de7fa16bf589b43ca634ed2e99521dbedd89c4d84c4db
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 870) what is this?
Submitted by
dwrensha
Submitted at
2026-09-27 18:55:47
Display reorder
866,702,39,296,644,291,112,798,202,135,585,765,703,271,348,69,174,778,416,671,667,529,266,392,607,569,393,687,32,769,638,740,555,5,4,852,597,167,551,387,110,30,748,519,502,109,664,208,7,707,750,813,577,821,56,495,207,279,213,447,464,126,710,298,239,848,541,55,486,784,285,231,521,514,593,374,753,355,125,681,67,165,445,163,365,646,452,861,734,485,816,399,547,50,504,799,758,225,316,336,406,383,417,367,580,562,44,293,775,737,106,444,511,858,380,9,111,143,824,37,605,662,484,814,509,648,242,270,744,114,711,217,59,757,650,475,371,515,666,715,719,158,831,146,366,20,498,454,154,686,792,800,840,258,426,105,244,827,45,763,3,493,353,334,660,144,142,625,807,863,345,29,745,204,282,362,313,508,272,716,423,804,6,89,27,608,793,627,216,459,196,736,853,494,694,137,92,83,433,665,746,237,450,773,709,838,280,90,604,809,19,150,308,487,695,783,467,587,573,438,682,839,116,62,611,183,752,817,468,788,129,865,762,566,384,818,52,162,796,767,811,512,797,141,713,491,87,836,815,870,305,326,630,347,203,651,254,401,301,224,253,672,21,275,528,422,219,322,639,245,579,307,209,726,101,31,626,329,172,549,462,443,578,273,152,343,851,693,61,299,460,633,823,328,199,263,594,747,236,122,544,41,635,647,151,350,310,193,706,603,759,84,250,98,58,632,13,294,567,206,782,397,856,473,825,714,235,71,489,320,297,115,652,654,117,844,497,349,720,220,76,284,787,615,570,801,330,257,249,176,697,598,354,51,477,656,288,701,2,205,123,404,482,364,140,214,28,760,201,624,234,780,785,138,398,304,373,119,95,68,281,653,621,16,524,315,400,588,616,227,265,803,75,418,469,478,561,527,517,846,859,768,215,256,360,81,436,510,306,341,191,318,596,136,476,673,589,675,36,171,668,499,210,518,449,403,377,741,828,274,342,24,430,338,749,808,200,669,575,591,756,822,717,351,25,278,466,303,240,197,14,718,121,619,358,375,238,72,620,531,407,677,453,309,721,722,411,230,128,226,63,177,537,425,97,536,776,385,124,161,560,268,684,38,492,781,160,222,441,645,712,255,622,834,134,806,70,159,323,419,546,325,190,394,841,173,361,149,833,78,168,335,300,674,533,642,391,8,283,545,378,369,43,421,448,609,85,670,458,248,148,286,93,857,241,23,409,472,166,91,655,532,730,582,637,548,574,571,64,501,772,481,368,789,657,269,850,277,679,381,812,18,623,457,181,564,649,327,120,395,613,212,586,372,22,617,534,157,543,530,455,727,847,610,15,729,556,46,153,192,410,689,185,520,864,264,500,539,732,104,57,424,311,431,680,795,526,849,704,295,352,396,559,34,754,451,490,359,456,770,584,862,488,221,723,690,49,629,317,612,698,777,312,843,133,738,819,405,223,35,156,332,606,88,786,324,724,261,292,218,402,17,79,739,195,175,832,640,470,379,725,429,688,259,550,82,287,641,413,552,661,461,590,731,414,108,708,363,42,742,790,743,692,465,794,251,576,182,233,247,232,73,474,198,618,558,188,446,572,118,408,557,131,830,40,439,802,178,540,869,523,581,130,289,685,705,229,48,10,513,761,835,771,0,867,243,631,96,842,699,66,766,516,276,228,643,333,855,267,155,102,860,86,80,180,1,764,344,319,440,260,600,503,346,595,211,65,415,507,496,805,194,339,382,252,170,542,854,568,26,614,189,428,356,774,321,376,728,179,554,735,696,77,412,186,11,100,337,184,599,386,432,700,390,107,53,483,442,755,103,506,663,837,139,420,691,601,113,60,302,525,169,820,340,779,147,246,479,370,262,357,33,427,463,437,94,471,187,388,145,634,676,583,553,54,751,314,636,829,658,791,602,127,628,99,592,565,74,480,522,434,826,12,535,132,389,164,810,845,678,47,290,659,505,683,331,538,733,868,435,563 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Monogenic cyclic-affine Eq677 magma of order 871. On Z/871, in construction labels, x*y = 230x + 635y + 1 (mod 871). Element 0 generates the whole magma; there are 792 generators and 1 idempotent element(s). For any element r, the generated submagma has size 871/gcd(871, (230+635-1)r+1). Both coefficients are units modulo 871, 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 758641 Eq677 instances, all 871 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 18:55:47 · history