Equation 677 Database

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Magma 3ddb8534a374…

magma 3ddb8534a374
Size
941
Isomorphism class hash
3ddb8534a37414fe9e7396aa3ac41886fead33d32c991a5210839d8e67af585c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 940) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 08:41:44
Display reorder
940,517,344,420,647,539,426,322,670,533,442,338,663,151,141,135,810,328,436,523,653,518,345,421,640,540,427,323,665,534,443,339,656,144,142,128,811,329,437,524,654,519,346,422,641,541,428,324,664,535,444,340,657,145,143,129,812,330,438,525,655,512,347,423,642,542,429,325,666,528,445,341,658,146,136,130,813,331,439,526,648,513,348,416,643,543,430,326,669,529,446,342,659,147,137,131,814,332,432,527,649,514,349,417,644,536,431,327,671,530,447,343,660,815,148,138,132,650,333,433,520,816,350,515,418,645,537,424,320,667,531,440,336,661,149,139,133,651,334,434,521,351,817,516,419,646,538,425,321,668,532,441,337,662,150,140,134,652,335,435,522,156,157,158,152,153,154,155,159,860,866,873,909,918,911,858,920,874,904,931,919,925,924,939,908,921,859,912,923,174,26,240,448,176,254,4,478,190,224,20,464,125,103,109,828,10,238,160,462,175,27,241,449,177,255,5,479,191,225,21,465,126,96,110,830,11,239,161,463,168,28,242,450,178,248,6,472,184,226,22,466,127,97,111,832,12,232,162,456,169,29,243,451,179,249,7,473,185,227,23,467,120,98,104,834,13,233,163,457,170,30,244,452,180,250,1,474,186,228,16,468,121,99,105,836,14,234,164,458,171,31,245,453,181,251,0,475,187,229,17,469,838,122,100,106,459,15,235,165,825,24,172,246,454,182,252,2,476,188,230,18,470,123,101,107,460,8,236,166,25,826,173,247,455,183,253,3,477,189,231,19,471,124,102,108,461,9,237,167,118,119,112,114,115,116,117,113,843,852,850,902,868,927,841,870,851,840,901,867,849,847,848,928,869,842,898,926,281,675,221,486,265,215,691,508,259,205,681,502,616,632,626,809,697,199,275,492,282,676,222,487,266,208,692,509,260,206,682,503,617,633,627,819,698,192,276,493,283,677,223,480,267,209,693,510,261,207,683,496,618,634,628,821,699,193,277,494,284,678,216,481,268,210,694,511,262,200,684,497,619,635,629,822,700,194,278,495,285,679,217,482,269,211,695,504,263,201,685,498,620,636,630,805,701,195,279,488,286,672,218,483,270,212,688,505,256,202,686,499,806,621,637,631,489,702,196,272,807,673,287,219,484,271,213,689,506,257,203,687,500,622,638,624,490,703,197,273,674,808,280,220,485,264,214,690,507,258,204,680,501,623,639,625,491,696,198,274,609,610,611,613,614,615,608,612,882,899,854,937,871,903,883,910,853,884,938,932,879,880,917,900,872,922,929,881,582,798,303,389,604,289,775,411,598,305,789,405,731,708,714,818,780,319,588,395,583,799,296,390,605,290,770,412,599,306,790,406,732,709,715,820,781,312,589,396,576,792,297,391,606,291,771,413,592,307,791,407,733,710,716,823,782,313,590,397,577,793,298,384,607,292,769,414,593,308,784,400,734,711,717,800,783,314,591,398,578,794,299,385,600,293,768,415,594,309,785,401,735,704,718,802,776,315,584,399,579,795,300,386,601,294,774,408,595,310,786,402,803,728,705,719,392,777,316,585,804,796,580,301,387,602,295,772,409,596,311,787,403,729,706,712,393,778,317,586,797,801,581,302,388,603,288,773,410,597,304,788,404,730,707,713,394,779,318,587,721,722,723,725,726,727,720,724,892,930,915,857,863,877,891,865,878,890,856,907,887,885,933,855,864,936,916,886,376,62,762,552,360,753,32,562,354,744,48,568,75,91,85,833,46,738,370,546,377,63,763,553,361,754,33,563,355,745,49,569,76,92,86,835,47,739,371,547,378,56,764,554,362,755,34,564,356,746,50,570,77,93,87,837,40,737,372,548,379,57,765,555,363,756,35,565,357,747,51,571,78,94,80,839,41,736,373,549,380,58,766,556,364,757,36,566,358,748,52,572,79,95,81,824,42,741,374,550,381,59,767,557,365,758,37,567,359,749,53,573,827,72,88,82,551,43,742,375,829,60,382,760,558,366,759,38,560,352,750,54,574,73,89,83,544,44,743,368,61,831,383,761,559,367,752,39,561,353,751,55,575,74,90,84,545,45,740,369,68,69,70,64,65,66,67,71,894,935,905,889,875,906,844,914,862,893,888,913,896,846,895,934,876,845,861,897 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 941 = 1 + 5*188, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#28c135c31c9c16f63ac84541dde3ead566850ad6b588a124a02a031b47e5c71c, M = {181} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 188): MacNeish's product over GF(4) x GF(47); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 101.

last edited by qawbecrdtey at 2026-10-07 08:41:46 · history