Equation 677 Database

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Magma 86a68a96b70b…

magma 86a68a96b70b
Size
973
Isomorphism class hash
86a68a96b70b25034a13fc244a491aea9fc04b75da530d52f757942fae06c96c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 972) what is this?
Submitted by
dwrensha
Submitted at
2026-09-27 19:02:05
Display reorder
824,883,649,729,201,443,702,333,958,72,487,712,90,241,574,877,255,344,814,134,67,486,905,483,705,548,317,822,610,954,809,445,542,242,614,664,893,459,365,530,811,276,81,927,673,523,339,85,41,150,938,655,358,141,7,148,444,944,245,410,284,567,738,967,889,3,405,309,503,123,273,959,625,376,87,32,11,812,935,685,393,500,111,31,634,916,187,415,24,247,792,70,873,453,427,422,224,178,33,885,543,433,820,267,296,308,929,701,699,19,515,714,38,918,553,735,464,621,223,516,894,310,388,706,27,726,160,892,773,569,9,43,326,462,869,61,351,796,189,732,155,856,821,759,329,154,256,716,922,441,384,576,521,620,145,915,35,378,724,681,532,426,842,797,397,428,139,656,800,890,537,396,476,17,572,210,830,40,394,206,425,47,562,868,477,547,570,555,188,676,859,1,825,648,787,490,734,909,290,481,82,184,970,165,941,265,511,264,757,311,764,867,122,665,678,561,720,670,851,320,412,558,585,680,540,948,507,623,482,114,36,69,850,519,399,694,823,99,120,849,525,379,506,449,231,658,882,791,617,274,164,827,498,854,689,406,55,739,424,135,902,182,383,672,174,198,170,895,661,605,606,485,508,96,937,103,375,790,179,193,8,896,713,535,748,539,762,598,844,162,348,279,22,183,492,920,132,386,2,327,472,248,884,340,400,730,80,708,205,846,335,408,660,53,133,343,923,325,765,314,657,608,28,839,501,347,108,697,584,13,921,779,359,186,292,780,480,913,435,659,784,971,203,682,898,465,457,161,467,810,59,955,619,357,113,169,578,6,908,300,345,97,100,448,788,831,577,409,700,687,4,338,837,235,381,216,633,158,298,840,137,390,334,509,566,115,881,571,469,760,597,544,107,876,270,575,146,237,173,420,945,157,356,772,709,208,175,862,559,366,249,307,62,628,942,117,374,778,703,110,215,888,489,367,294,204,644,328,956,56,475,666,691,538,640,961,172,635,440,277,286,195,897,240,387,564,159,128,293,917,280,354,618,769,266,646,911,719,517,14,12,94,243,828,51,647,226,63,79,688,875,109,741,536,219,526,534,841,613,373,968,715,590,504,833,549,711,234,129,26,710,864,98,653,766,58,104,432,919,77,677,588,257,696,268,866,285,382,0,591,261,278,903,147,777,65,799,336,283,964,305,541,269,48,153,190,863,423,369,71,337,73,220,901,667,693,470,817,466,782,953,93,371,121,721,213,18,857,10,439,416,675,674,592,952,227,372,116,603,138,125,845,192,493,808,106,251,758,934,429,355,221,332,686,722,962,589,402,518,437,118,456,906,177,346,754,763,331,450,907,83,361,171,413,554,438,891,471,611,654,627,281,263,931,601,789,630,609,596,180,924,695,395,826,322,442,323,861,222,966,126,68,550,233,829,803,421,718,579,756,54,939,607,370,624,639,478,546,925,631,350,494,149,306,91,910,152,641,102,545,316,468,947,731,587,196,497,321,728,899,495,463,612,793,228,86,835,202,551,452,645,143,510,865,785,407,211,272,690,752,936,212,801,131,727,84,112,926,531,398,29,95,638,704,949,217,795,76,775,163,253,951,447,377,552,533,804,622,838,88,783,446,105,768,770,872,250,392,324,751,502,474,965,46,368,166,491,496,522,930,20,723,304,74,484,130,836,565,353,60,431,301,616,855,743,363,45,37,218,556,879,330,380,434,252,246,49,946,969,807,636,342,271,303,887,513,385,92,199,21,586,858,207,362,34,282,454,604,870,66,411,742,461,57,528,950,595,683,299,473,514,740,874,679,753,259,479,774,414,848,417,360,191,745,52,313,957,643,404,39,781,418,23,878,275,771,512,144,798,580,963,755,813,136,615,42,652,843,230,629,582,5,750,698,943,749,557,176,805,291,794,847,127,352,289,124,668,318,933,737,403,594,209,816,101,912,315,529,156,302,520,776,928,197,717,254,297,430,568,932,815,505,600,287,168,238,860,78,581,319,455,662,75,880,30,563,642,733,602,225,914,142,401,488,527,16,692,972,761,364,458,419,341,200,834,167,671,802,573,632,44,960,25,593,524,262,650,64,940,295,389,229,669,436,746,852,637,499,239,312,786,140,871,707,451,244,214,460,258,832,15,747,151,663,236,806,853,260,599,181,232,89,185,904,725,391,736,119,626,818,886,767,819,50,651,560,288,900,583,349,684,194,744 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Monogenic cyclic-affine Eq677 magma of order 973. On Z/973, in construction labels, x*y = 235x + 675y + 1 (mod 973). Element 0 generates the whole magma; there are 828 generators and 1 idempotent element(s). For any element r, the generated submagma has size 973/gcd(973, (235+675-1)r+1). Both coefficients are units modulo 973, 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 946729 Eq677 instances, all 973 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 19:02:05 · history