Equation 677 Database

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Magma d9884bd6ceb1…

magma d9884bd6ceb1
Size
909
Isomorphism class hash
d9884bd6ceb1d7d4c408689fef76dbb56bcd359d83857e687f500e1f04c5ecff
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 12:36:12
Display reorder
803,804,805,806,807,801,800,802,908,173,427,574,382,443,183,558,368,544,421,189,366,560,437,167,352,350,320,334,174,428,575,383,444,176,559,369,545,422,190,367,561,438,160,353,351,321,335,175,429,568,376,445,177,552,370,546,423,191,360,562,439,161,354,344,322,328,168,430,569,377,446,178,553,371,547,416,184,361,563,432,162,355,345,323,329,169,431,570,378,447,179,554,372,548,417,185,362,564,433,163,356,346,324,330,170,424,571,379,440,180,555,373,549,418,186,363,357,565,434,164,347,325,331,358,425,171,572,380,441,181,556,374,550,419,187,364,566,435,165,348,326,332,426,359,172,573,381,442,182,557,375,551,420,188,365,567,436,166,349,327,333,343,336,337,339,340,341,342,338,871,868,869,858,870,843,832,840,854,836,842,839,837,838,841,904,894,895,893,896,53,220,604,392,198,37,588,386,582,214,43,402,598,204,59,408,109,125,119,54,221,605,393,199,38,589,387,583,215,44,403,599,205,60,409,110,126,112,55,222,606,394,192,39,590,388,576,208,45,404,592,206,61,410,111,127,113,48,223,607,395,193,32,591,389,577,209,46,405,593,207,62,411,104,120,114,49,216,600,396,194,33,584,390,578,210,47,406,594,200,63,412,105,121,115,50,217,601,397,195,34,585,391,579,211,40,407,413,595,201,56,106,122,116,414,218,51,602,398,196,35,586,384,580,212,41,400,596,202,57,107,123,117,219,415,52,603,399,197,36,587,385,581,213,42,401,597,203,58,108,124,118,102,103,96,98,99,100,101,97,874,861,859,880,866,875,879,865,881,862,873,863,860,864,872,847,828,831,829,830,88,614,153,230,627,72,137,236,131,616,66,252,147,637,82,246,28,6,12,89,615,154,231,628,73,138,237,132,618,67,253,148,638,83,247,29,7,13,90,613,155,224,629,74,139,238,133,619,68,254,149,639,84,240,30,1,14,91,611,156,225,630,75,140,239,134,620,69,255,150,632,85,241,31,0,15,92,612,157,226,631,76,141,232,135,621,70,248,151,633,86,242,24,2,8,93,610,158,227,625,77,142,233,128,622,71,249,243,144,634,87,25,3,9,244,608,94,159,228,624,78,143,234,129,623,64,250,145,635,80,26,4,10,609,245,95,152,229,626,79,136,235,130,617,65,251,146,636,81,27,5,11,21,22,23,17,18,19,20,16,851,856,857,852,853,902,901,903,888,907,889,892,906,891,890,887,886,884,885,883,540,476,283,486,454,524,267,492,261,470,518,508,277,460,534,502,309,299,293,541,477,284,487,455,525,268,493,262,471,519,509,278,461,535,503,310,300,294,542,478,285,480,448,526,269,494,263,464,512,510,279,462,528,496,311,301,295,543,479,286,481,449,527,270,495,256,465,513,511,272,463,529,497,304,302,288,536,472,287,482,450,520,271,488,257,466,514,504,273,456,530,498,305,303,289,537,473,280,483,451,521,264,489,258,467,515,505,499,274,457,531,306,296,290,500,474,538,281,484,452,522,265,490,259,468,516,506,275,458,532,307,297,291,475,501,539,282,485,453,523,266,491,260,469,517,507,276,459,533,308,298,292,314,315,316,318,319,312,313,317,867,878,877,876,882,833,844,850,855,846,835,848,845,849,834,905,900,898,899,897,683,689,687,693,691,682,685,692,684,688,681,694,686,690,680,695,698,697,696,711,716,714,719,717,709,713,718,712,715,710,704,702,703,701,705,708,707,706,722,729,727,733,731,721,725,732,724,728,720,734,726,730,723,735,738,737,736,742,749,747,753,751,741,745,752,744,748,740,754,746,750,743,755,758,757,756,762,769,767,773,771,761,765,772,764,768,760,774,766,770,763,775,778,777,776,782,789,787,793,791,781,785,792,784,788,780,794,795,786,790,783,798,797,796,655,649,642,647,653,651,640,645,652,644,648,641,654,646,650,643,658,657,656,669,675,662,667,673,671,660,665,672,664,668,661,674,666,670,663,678,677,676,679,699,700,759,779,799,659,739,813,819,817,809,822,814,810,821,808,818,815,820,816,823,812,811,826,824,827,825 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 = {19, 39, 59, 79, 99, 116, 136, 156, 185} 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 12:36:18 · history