Equation 677 Database

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Magma fe8e8d18e472…

magma fe8e8d18e472
Size
909
Isomorphism class hash
fe8e8d18e472c16f06b38f31a342dbaac1b4012a4d71d652b452940e0cd8282c
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 11:19:26
Display reorder
805,806,807,801,800,802,803,804,908,78,354,9,280,376,25,264,64,154,132,148,80,360,274,19,94,3,258,370,79,355,10,281,377,26,265,65,155,133,149,81,361,275,20,95,4,259,371,72,356,11,282,378,27,266,66,156,134,150,82,362,276,21,88,5,260,372,73,357,12,283,379,28,267,67,157,135,151,83,363,277,22,89,6,261,373,74,358,13,284,380,29,268,68,158,128,144,84,364,278,23,90,7,262,374,75,359,14,285,381,30,269,69,159,129,145,16,85,365,279,375,91,1,263,17,352,76,15,286,382,31,270,70,152,130,146,86,366,272,368,92,0,256,353,18,77,8,287,383,24,271,71,153,131,147,87,367,273,369,93,2,257,137,138,139,141,142,143,136,140,863,870,862,861,874,844,834,830,840,831,843,839,832,829,833,884,888,883,885,890,469,197,412,173,219,390,183,475,347,325,341,453,203,167,396,459,406,189,213,470,198,413,174,220,391,176,476,348,326,342,454,204,160,397,460,407,190,214,471,199,414,175,221,384,177,477,349,327,343,455,205,161,398,461,400,191,215,464,192,415,168,222,385,178,478,350,320,336,448,206,162,399,462,401,184,208,465,193,408,169,223,386,179,479,351,321,337,449,207,163,392,463,402,185,209,466,194,409,170,216,387,180,472,344,322,338,393,450,200,164,210,456,403,186,394,195,467,410,171,217,388,181,473,345,323,339,451,201,165,211,457,404,187,196,395,468,411,172,218,389,182,474,346,324,340,452,202,166,212,458,405,188,330,331,332,334,335,328,329,333,864,860,873,876,868,869,866,875,859,871,867,858,872,877,865,842,828,845,837,838,573,484,557,511,603,639,630,615,622,500,580,495,547,551,597,554,519,589,564,574,485,558,504,604,632,631,608,623,501,581,488,548,550,598,549,512,590,565,575,486,559,505,605,633,624,609,616,502,582,489,521,538,599,529,513,591,566,568,487,543,506,606,634,625,610,617,503,583,490,522,539,592,525,514,584,567,569,481,544,507,607,635,626,611,618,496,576,491,523,540,593,526,515,585,561,570,480,545,508,600,636,627,612,619,497,577,594,492,524,541,560,527,516,586,595,482,571,546,509,601,637,628,613,620,498,578,493,520,542,562,528,517,587,483,596,572,556,510,602,638,629,614,621,499,579,494,552,555,563,553,518,588,535,536,537,531,532,533,534,530,854,853,857,855,856,906,904,895,903,902,896,899,897,905,898,907,894,901,893,900,34,296,242,424,306,232,434,40,110,126,96,56,290,418,226,50,248,440,312,35,297,243,425,307,233,435,41,111,127,97,57,291,419,227,51,249,441,313,36,298,244,426,308,234,436,42,104,120,98,58,292,420,228,52,250,442,314,37,299,245,427,309,235,437,43,105,121,99,59,293,421,229,53,251,443,315,38,300,246,428,310,236,438,44,106,122,100,60,294,422,230,54,252,444,316,39,301,247,429,311,237,439,45,107,123,101,231,61,295,423,317,55,253,445,224,302,32,240,430,304,238,432,46,108,124,102,62,288,416,318,48,254,446,303,225,33,241,431,305,239,433,47,109,125,103,63,289,417,319,49,255,447,119,112,113,115,116,117,118,114,881,882,880,879,878,848,851,849,852,850,835,846,841,836,847,889,891,887,892,886,664,705,681,799,735,697,783,658,766,736,752,648,719,785,691,642,675,769,721,665,706,682,792,728,698,776,659,767,737,753,649,712,786,692,643,676,770,722,666,707,683,793,729,699,777,660,760,738,754,650,713,787,693,644,677,771,723,667,708,684,794,730,700,778,661,761,739,755,651,714,788,694,645,678,772,724,668,709,685,795,731,701,779,662,762,740,756,652,715,789,695,646,679,773,725,669,710,686,796,732,702,780,663,763,741,757,688,653,716,790,726,647,672,774,689,711,670,687,797,733,703,781,656,764,742,758,654,717,791,727,641,673,775,704,690,671,680,798,734,696,782,657,765,743,759,655,718,784,720,640,674,768,749,750,751,745,746,747,748,744,823,824,818,821,825,813,814,811,817,809,827,826,819,820,822,808,816,810,815,812 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 = {9, 29, 49, 69, 89, 109, 130, 150, 169} 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 11:19:28 · history