Equation 677 Database

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Magma 1d93d0ac63d8…

magma 1d93d0ac63d8
Size
909
Isomorphism class hash
1d93d0ac63d8df2bea1fb1baae2c6c4e0c8fe82fc3195e53a38f31291f25f72b
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
2026-10-06 09:15:05
Display reorder
803,804,805,806,807,801,800,802,908,322,99,287,162,338,168,257,105,433,431,417,271,184,121,328,178,115,344,273,323,100,280,163,339,169,258,106,434,424,418,264,185,122,329,179,116,345,274,324,101,281,164,340,170,259,107,435,425,419,265,186,123,330,180,117,346,275,325,102,282,165,341,171,260,108,436,426,420,266,187,124,331,181,118,347,276,326,103,283,166,342,172,261,109,437,427,421,267,188,125,332,182,119,348,277,327,96,284,167,343,173,262,110,438,428,422,333,268,189,126,278,183,112,349,334,97,320,285,160,336,174,263,111,439,429,423,269,190,127,279,176,113,350,98,335,321,286,161,337,175,256,104,432,430,416,270,191,120,272,177,114,351,446,447,440,442,443,444,445,441,875,859,880,882,881,828,847,845,846,841,849,851,850,848,852,892,888,891,890,883,311,415,476,198,301,204,454,401,57,35,41,460,220,399,317,214,385,295,470,304,408,477,199,302,205,455,402,58,36,42,461,221,392,318,215,386,288,471,305,409,478,192,303,206,448,403,59,37,43,462,222,393,319,208,387,289,464,306,410,479,193,296,207,449,404,60,38,44,463,223,394,312,209,388,290,465,307,411,472,194,297,200,450,405,61,39,45,456,216,395,313,210,389,291,466,308,412,473,195,298,201,451,406,62,32,46,314,457,217,396,467,211,390,292,315,413,309,474,196,299,202,452,407,63,33,47,458,218,397,468,212,391,293,414,316,310,475,197,300,203,453,400,56,34,40,459,219,398,469,213,384,294,50,51,52,54,55,48,49,53,879,860,866,869,872,861,870,864,873,877,862,868,865,878,874,840,844,837,834,831,545,570,554,568,615,613,639,614,612,519,528,597,506,508,510,537,524,571,516,546,574,555,572,619,617,632,618,616,515,529,598,507,509,511,538,525,575,512,547,578,556,576,623,621,633,622,620,483,530,599,486,491,497,539,526,579,504,548,582,557,580,627,625,634,626,624,482,531,592,487,492,498,540,527,583,505,549,586,558,584,631,629,635,630,628,484,532,593,488,493,499,541,521,587,501,550,590,559,588,603,600,636,602,601,485,533,495,594,489,494,502,542,520,591,496,562,551,552,561,607,605,637,606,604,481,534,595,490,480,503,543,522,563,566,500,544,553,564,611,609,638,610,608,517,535,596,513,514,518,536,523,567,565,569,573,581,585,589,560,577,857,853,856,855,854,903,895,901,894,902,899,905,906,897,904,898,907,900,896,893,79,159,354,255,95,241,370,145,5,21,27,376,239,143,65,225,129,81,360,72,152,355,248,88,242,371,146,6,22,28,377,232,136,66,226,130,82,361,73,153,356,249,89,243,372,147,7,23,29,378,233,137,67,227,131,83,362,74,154,357,250,90,244,373,148,1,16,30,379,234,138,68,228,132,84,363,75,155,358,251,91,245,374,149,0,17,31,380,235,139,69,229,133,85,364,76,156,359,252,92,246,375,150,2,18,24,70,381,236,140,365,230,134,86,71,157,77,352,253,93,247,368,151,3,19,25,382,237,141,366,231,135,87,158,64,78,353,254,94,240,369,144,4,20,26,383,238,142,367,224,128,80,10,11,12,14,15,8,9,13,871,867,863,858,876,836,829,833,842,839,835,830,832,838,843,889,887,884,885,886,761,729,791,759,792,747,698,715,661,651,645,762,745,713,679,731,699,765,766,763,730,793,760,794,748,691,716,662,652,646,764,746,714,680,732,700,768,767,675,723,782,754,781,749,692,717,663,653,647,686,739,707,681,733,701,770,769,676,724,784,755,783,750,693,718,664,654,648,687,740,708,682,734,702,772,771,677,725,786,756,785,751,694,719,657,655,641,688,741,709,683,735,703,774,773,674,726,788,757,787,752,695,720,658,656,642,684,689,742,710,775,736,704,776,685,727,673,790,758,789,753,696,721,659,649,643,690,743,711,777,737,705,778,728,678,795,798,797,799,796,697,722,660,650,644,640,744,712,779,738,706,780,666,667,668,670,671,672,665,669,814,810,819,824,820,808,825,817,821,812,809,826,816,815,822,823,813,827,818,811 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#28c135c31c9c16f63ac84541dde3ead566850ad6b588a124a02a031b47e5c71c, M = {8, 28, 48, 68, 88, 108, 129, 149, 173} 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 2026-10-06 09:15:06 · history