Equation 677 Database

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Magma 113661e3b938…

magma 113661e3b938
Size
931
Isomorphism class hash
113661e3b938cb839d91f312fcc8c348468cbe031fee8240447127ad726c24c5
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 930) what is this?
Submitted by
dwrensha
Submitted at
2026-09-27 18:56:44
Display reorder
752,861,922,651,416,395,508,728,800,525,216,712,298,702,318,790,224,373,458,461,201,895,814,248,95,700,509,514,534,864,616,313,48,171,406,269,771,659,566,96,900,696,203,843,622,578,724,45,279,607,857,501,204,229,311,328,686,798,387,920,609,317,68,559,774,610,717,156,667,430,474,826,61,137,295,467,575,396,930,513,107,350,637,605,24,760,357,547,199,624,249,142,841,91,20,434,141,899,504,863,218,445,554,697,672,384,801,139,747,162,256,110,154,775,671,228,921,564,98,191,813,737,523,43,165,556,148,873,417,397,392,232,563,716,758,916,669,344,341,490,692,832,435,234,640,244,684,408,856,260,391,512,533,183,901,793,284,113,754,455,496,498,785,21,331,561,117,388,233,823,695,584,150,888,678,293,867,16,596,652,576,261,571,770,537,222,283,383,310,650,828,423,896,39,389,176,29,852,26,735,84,739,412,438,805,97,155,223,539,755,360,926,549,125,404,709,587,619,816,393,439,253,570,231,106,865,127,10,488,87,923,468,766,254,463,482,643,654,348,833,175,639,90,202,92,118,851,707,246,891,51,80,281,799,647,541,567,111,538,112,782,327,415,320,304,2,680,827,910,687,398,413,472,656,877,471,252,694,190,666,372,769,296,409,440,479,291,907,835,194,131,682,527,478,462,859,562,349,615,63,370,197,802,731,602,78,918,660,257,787,568,614,706,28,243,19,825,447,240,211,329,418,740,878,333,914,591,335,158,613,765,0,753,138,685,394,528,840,133,173,277,485,12,324,925,459,143,332,655,569,583,795,429,457,181,33,213,70,788,163,572,542,159,905,432,821,290,481,536,715,636,312,874,85,657,144,274,74,82,764,743,264,903,582,62,245,834,683,433,621,57,520,76,849,363,307,374,250,22,644,806,904,705,326,359,454,746,778,507,270,748,262,648,336,824,206,427,494,551,273,913,876,230,149,736,473,460,552,772,598,367,36,135,352,287,844,641,620,132,906,642,221,847,604,47,634,594,225,625,804,483,258,265,401,400,704,776,369,890,42,407,140,577,817,592,645,66,631,376,492,870,169,65,205,557,27,414,924,495,161,386,727,7,4,837,339,475,235,588,195,160,862,73,590,470,105,887,522,808,200,499,464,661,744,402,779,121,675,72,220,56,172,819,653,282,915,23,170,209,880,719,451,37,129,502,166,762,399,325,428,196,50,734,838,898,723,380,431,436,710,853,543,288,676,208,630,426,803,242,319,548,497,255,919,781,266,167,664,545,442,516,811,49,385,597,81,334,251,871,677,53,60,894,750,185,767,31,30,688,13,207,589,829,519,276,193,347,382,668,850,405,908,573,353,122,14,797,628,663,120,703,358,456,783,79,83,259,503,44,378,928,531,179,314,673,17,52,879,375,493,289,18,303,124,768,109,608,524,177,911,486,842,236,517,518,733,726,366,854,157,693,126,292,164,136,796,689,300,885,600,152,299,777,629,469,603,75,484,130,815,309,343,356,268,617,698,868,892,741,308,377,544,674,759,453,180,730,280,738,390,845,278,337,476,443,237,882,848,302,59,718,491,550,480,807,1,403,41,153,316,215,789,713,25,114,883,732,275,822,6,15,742,612,189,9,866,555,294,247,419,364,632,763,315,884,627,425,104,46,831,11,681,174,649,340,546,860,115,101,187,449,611,342,927,441,71,368,745,32,601,780,411,511,217,606,285,88,820,145,626,452,123,893,450,869,272,535,446,679,708,330,756,67,711,54,238,146,100,830,725,192,897,3,134,263,855,665,487,40,147,466,94,794,345,361,410,214,599,662,784,886,633,362,323,526,638,810,489,198,658,226,720,354,881,188,355,530,515,219,889,761,212,77,646,437,532,444,839,580,421,579,99,424,305,858,749,5,168,912,714,239,809,586,560,670,558,297,34,791,465,186,301,365,346,722,818,351,902,38,371,86,595,872,574,699,102,721,322,510,773,151,119,241,521,593,306,929,477,89,422,691,623,565,846,321,529,271,8,267,178,792,55,35,506,69,917,540,786,182,553,500,751,690,420,812,103,729,108,184,128,64,875,635,210,909,618,116,227,757,701,505,585,93,448,58,836,381,379,338,286,581 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Monogenic cyclic-affine Eq677 magma of order 931. On Z/931, in construction labels, x*y = 900x + 402y + 1 (mod 931). Element 0 generates the whole magma; there are 756 generators and 1 idempotent element(s). For any element r, the generated submagma has size 931/gcd(931, (900+402-1)r+1). Both coefficients are units modulo 931, 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 866761 Eq677 instances, all 931 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 18:56:44 · history