Equation 677 Database

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Magma 87af687fd76c…

magma 87af687fd76c
Size
909
Isomorphism class hash
87af687fd76ced517a1bcf93ccd5365ae49c7a2a9f652d4f23b23e1295ddbae9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 908) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 07:43:55
Display reorder
806,807,801,800,802,803,804,805,908,511,495,497,351,368,191,288,335,366,175,318,302,337,352,177,304,321,382,161,504,488,498,344,369,184,289,328,367,168,319,303,338,353,178,305,322,383,162,505,489,499,345,370,185,290,329,360,169,312,296,339,354,179,306,323,376,163,506,490,500,346,371,186,291,330,361,170,313,297,340,355,180,307,324,377,164,507,491,501,347,372,187,292,331,362,171,314,298,341,356,181,308,325,378,165,508,492,502,348,373,188,293,332,363,172,315,166,299,342,357,182,309,326,379,509,493,503,349,374,189,294,333,364,173,316,167,300,343,358,183,310,327,380,510,494,496,350,375,190,295,334,365,174,317,160,301,336,359,176,311,320,381,480,481,482,484,485,486,487,483,874,875,873,878,862,842,835,845,838,843,836,846,839,844,837,884,888,885,887,886,198,220,204,397,88,28,55,407,66,12,39,61,391,72,22,45,413,82,6,199,221,205,398,89,29,48,400,67,13,32,62,384,73,23,46,414,83,7,192,222,206,399,90,30,49,401,68,14,33,63,385,74,16,47,415,84,1,193,223,207,392,91,31,50,402,69,15,34,56,386,75,17,40,408,85,0,194,216,200,393,92,24,51,403,70,8,35,57,387,76,18,41,409,86,2,195,217,201,394,93,25,52,404,71,9,36,3,58,388,77,19,42,410,87,196,218,202,395,94,26,53,405,64,10,37,4,59,389,78,20,43,411,80,197,219,203,396,95,27,54,406,65,11,38,5,60,390,79,21,44,412,81,213,214,215,209,210,211,212,208,859,861,858,867,877,868,876,871,866,869,864,872,865,870,863,841,831,840,830,829,103,125,109,574,596,245,602,553,629,229,618,588,567,614,251,632,551,591,235,96,126,110,575,597,246,603,552,630,230,619,587,561,615,252,633,550,589,236,97,127,111,568,598,247,604,554,631,231,620,577,560,609,253,634,544,576,237,98,120,104,569,599,240,605,555,624,224,621,579,562,608,254,635,545,578,238,99,121,105,570,593,241,606,556,625,225,622,581,563,610,255,636,546,580,239,100,122,106,571,592,242,607,557,626,226,623,232,583,564,611,248,637,547,582,101,123,107,572,594,243,600,558,627,227,616,233,585,565,612,249,638,548,584,102,124,108,573,595,244,601,559,628,228,617,234,590,566,613,250,639,549,586,118,119,112,114,115,116,117,113,833,834,832,856,857,906,905,902,896,900,899,903,897,901,898,895,904,907,894,883,540,524,534,461,270,422,147,471,286,444,131,153,455,272,428,137,477,256,438,541,525,535,462,271,423,148,464,287,445,132,154,448,273,429,138,478,257,439,542,526,528,463,264,416,149,465,280,446,133,155,449,274,430,139,479,258,432,543,527,529,456,265,417,150,466,281,447,134,156,450,275,431,140,472,259,433,536,520,530,457,266,418,151,467,282,440,135,157,451,276,424,141,473,260,434,537,521,531,458,267,419,144,468,283,441,128,435,158,452,277,425,142,474,261,538,522,532,459,268,420,145,469,284,442,129,436,159,453,278,426,143,475,262,539,523,533,460,269,421,146,470,285,443,130,437,152,454,279,427,136,476,263,517,518,519,513,514,515,516,512,880,881,879,860,882,828,855,849,852,847,853,850,851,848,854,892,890,893,889,891,798,782,784,659,751,705,691,643,767,735,675,697,665,753,719,681,649,737,721,799,783,785,660,744,706,692,644,760,728,676,698,666,754,712,682,650,738,722,792,776,786,661,745,707,693,645,761,729,677,699,667,755,713,683,651,739,723,793,777,787,662,746,708,694,646,762,730,678,700,668,756,714,684,652,740,724,794,778,788,663,747,709,695,647,763,731,679,701,669,757,715,685,653,741,725,795,779,789,656,748,710,688,641,764,732,672,726,702,670,758,716,686,654,742,796,780,790,657,749,711,689,640,765,733,673,727,703,671,759,717,687,655,743,797,781,791,658,750,704,690,642,766,734,674,720,696,664,752,718,680,648,736,775,768,769,771,772,773,774,770,815,813,816,819,811,818,810,821,809,822,826,824,825,823,827,812,817,808,820,814 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 909 = 9 + 5*180, 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#2fbf4aeb3299bf5cd73928e6481588671312464fd86e85db3182e3511e27e065, M = {3, 23, 43, 63, 83, 103, 123, 143, 168} 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, 180): MacNeish's product over GF(4) x GF(9) x GF(5); GF(4) = F_2[x]/(x^2 + x + 1), GF(9) = F_3[x]/(x^2 + 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 2026-10-08 07:43:56 · history