Equation 677 Database

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Magma c6ec3cb4f798…

magma c6ec3cb4f798
Size
949
Isomorphism class hash
c6ec3cb4f798805a16813b66e943c3583d00fcabd9253e7fbf21ac5189392652
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 948) what is this?
Submitted by
dwrensha
Submitted at
2026-09-27 18:58:56
Display reorder
944,493,11,613,769,902,790,241,155,651,407,862,165,941,170,59,710,486,99,646,247,287,265,702,765,397,850,173,70,663,442,334,254,394,826,136,507,715,303,132,597,31,145,104,472,693,580,773,895,699,79,500,609,355,62,760,537,814,492,768,240,418,940,709,645,264,396,69,333,825,714,596,103,579,698,608,759,491,417,644,68,713,578,758,643,577,576,801,802,856,545,791,926,74,857,3,278,546,821,911,792,316,809,927,600,120,75,195,489,858,934,727,4,465,555,279,589,750,547,56,142,822,275,86,912,682,560,793,906,259,317,358,37,810,345,90,928,294,337,601,181,467,121,217,876,76,374,625,196,540,915,490,512,460,859,300,273,923,65,371,728,378,637,5,864,368,466,565,689,556,838,17,280,719,667,590,150,673,751,175,329,548,361,788,57,763,392,143,498,250,823,415,799,276,118,553,84,35,477,913,381,687,671,390,551,561,518,830,794,782,48,907,528,520,260,533,290,318,322,94,347,888,832,38,622,439,811,640,724,346,365,796,91,450,656,929,21,233,295,805,784,338,629,268,602,426,453,182,882,50,468,678,526,122,947,434,218,946,909,877,847,352,77,192,342,375,495,530,626,88,705,197,209,647,541,13,522,916,149,737,479,867,224,513,615,262,461,114,9,860,245,661,301,771,535,274,696,756,924,314,932,54,904,292,372,310,874,729,359,413,379,780,320,638,19,424,1,190,207,865,243,312,369,188,400,455,402,24,566,157,96,690,112,920,557,457,326,827,653,349,6,421,83,281,404,633,720,409,890,668,212,841,591,26,236,151,852,834,674,108,745,752,568,742,176,167,40,330,201,284,549,159,387,362,943,612,789,650,164,58,98,298,764,172,441,393,506,131,144,692,894,499,61,813,239,708,395,824,102,607,416,712,642,800,544,73,277,922,808,119,488,726,554,749,141,85,559,258,36,101,336,478,875,624,914,459,272,382,636,367,688,16,666,672,328,787,391,249,798,552,476,686,562,829,47,519,289,93,831,438,723,795,655,232,783,267,452,49,525,433,908,351,341,529,704,658,521,736,223,261,8,660,534,755,931,291,873,412,319,423,206,311,399,23,95,919,325,348,82,632,889,840,235,833,744,741,39,283,386,611,163,297,440,130,893,812,406,606,641,72,807,725,140,257,335,623,271,366,665,786,797,685,46,92,722,231,451,432,340,657,222,659,930,411,205,22,324,631,234,740,385,296,892,605,806,256,270,785,45,230,339,670,204,630,384,604,269,229,203,603,214,948,427,816,428,454,482,817,183,843,429,883,126,443,51,572,483,469,593,818,679,509,184,515,447,844,123,28,430,198,717,884,435,870,127,219,238,444,935,305,52,910,584,573,878,153,484,848,134,470,353,938,594,66,854,819,193,587,680,343,215,510,376,836,185,496,33,516,531,620,448,627,676,845,89,147,124,706,308,29,186,110,419,210,106,199,648,504,718,542,747,885,14,474,436,523,734,871,917,754,128,138,683,220,738,43,227,480,570,445,868,582,936,225,618,306,514,732,53,616,775,899,251,777,585,462,178,574,115,897,879,10,901,154,861,169,485,246,701,849,662,253,135,302,30,471,772,78,354,536,767,939,263,332,595,697,502,67,757,575,855,925,2,820,315,599,194,933,464,588,55,286,681,905,357,344,293,180,216,373,539,511,299,64,377,863,564,837,730,161,174,360,762,497,414,117,34,380,389,517,781,527,532,321,887,621,639,364,449,20,804,628,425,881,677,0,945,846,191,494,87,208,12,148,866,614,125,244,770,695,313,903,309,370,779,18,189,242,187,401,156,111,456,652,420,403,408,211,25,851,107,567,166,200,158,942,649,97,171,505,691,60,707,113,711,543,921,487,748,558,100,886,458,635,15,327,248,475,828,288,437,654,266,524,350,703,735,7,766,872,422,398,918,81,839,743,282,162,129,405,71,139,634,664,684,721,431,221,410,323,739,891,255,44,669,383,228,213,815,481,842,137,571,592,508,446,27,716,869,237,304,583,152,133,937,853,598,226,835,32,619,675,146,307,109,105,503,746,473,733,753,694,42,569,581,617,731,774,776,177,896,900,168,700,252,41,80,778,331,501,586,202,610,463,285,356,179,550,63,563,160,761,116,388,538,898,363,803,880 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Monogenic cyclic-affine Eq677 magma of order 949. On Z/949, in construction labels, x*y = 373x + 193y + 1 (mod 949). Element 0 generates the whole magma; there are 864 generators and 1 idempotent element(s). For any element r, the generated submagma has size 949/gcd(949, (373+193-1)r+1). Both coefficients are units modulo 949, 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 900601 Eq677 instances, all 949 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 18:58:56 · history