Equation 677 Database

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Magma c9413a95eeb2…

magma c9413a95eeb2
Size
909
Isomorphism class hash
c9413a95eeb2583585c6688b48a63ee54da58f59994f131c2f069512e2038faf
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 10:53:45
Display reorder
802,803,804,805,806,807,801,800,908,203,37,125,257,389,395,411,119,287,59,213,103,197,273,43,53,219,271,109,204,38,126,258,390,396,412,112,280,60,214,96,198,274,44,54,220,264,110,205,39,127,259,391,397,413,113,281,61,215,97,199,275,45,55,221,265,111,206,32,120,260,384,398,414,114,282,62,208,98,192,276,46,48,222,266,104,207,33,121,261,385,399,415,115,283,63,209,99,193,277,47,49,223,267,105,200,34,122,262,386,392,408,116,284,56,210,40,100,194,278,106,50,216,268,41,35,201,123,263,387,393,409,117,285,57,211,101,195,279,107,51,217,269,36,42,202,124,256,388,394,410,118,286,58,212,102,196,272,108,52,218,270,404,405,406,400,401,402,403,407,867,881,880,882,871,841,833,831,840,837,832,830,839,836,834,883,885,886,884,887,420,245,522,490,291,297,313,516,500,229,442,538,426,506,251,235,436,484,532,421,246,523,491,292,298,314,517,501,230,443,539,427,507,252,236,437,485,533,422,247,524,492,293,299,315,518,502,231,444,540,428,508,253,237,438,486,534,423,240,525,493,294,300,316,519,503,224,445,541,429,509,254,238,439,487,535,416,241,526,494,295,301,317,512,496,225,446,542,430,510,255,239,432,480,528,417,242,527,495,288,302,318,513,497,226,447,248,543,431,511,529,232,433,481,249,243,418,520,488,289,303,319,514,498,227,440,536,424,504,530,233,434,482,244,250,419,521,489,290,296,312,515,499,228,441,537,425,505,531,234,435,483,306,307,308,310,311,304,305,309,874,868,869,870,878,863,872,861,859,877,862,860,858,879,873,828,849,829,838,835,344,136,584,625,549,554,573,602,595,146,328,620,338,576,130,152,322,623,634,345,137,585,626,550,555,574,603,596,147,329,619,339,578,131,153,323,621,635,346,138,586,627,551,556,575,604,597,148,330,609,340,579,132,154,324,608,636,347,139,587,628,547,557,568,605,598,149,331,611,341,580,133,155,325,610,637,348,140,588,629,546,558,569,606,599,150,332,613,342,581,134,156,326,612,638,349,141,589,630,544,559,570,607,593,151,333,135,615,343,582,639,157,327,614,128,142,350,590,631,545,553,571,600,592,144,334,617,336,583,632,158,320,616,143,129,351,591,624,548,552,572,601,594,145,335,622,337,577,633,159,321,618,562,563,564,566,567,561,560,565,856,854,853,855,857,900,907,899,902,894,897,898,903,904,895,896,906,901,905,893,14,66,352,161,474,468,458,366,191,88,16,368,1,177,72,82,30,175,382,15,67,353,162,475,469,459,367,184,89,17,369,0,178,73,83,31,168,383,8,68,354,163,476,470,460,360,185,90,18,370,2,179,74,84,24,169,376,9,69,355,164,477,471,461,361,186,91,19,371,3,180,75,85,25,170,377,10,70,356,165,478,464,462,362,187,92,20,372,4,181,76,86,26,171,378,11,71,357,166,479,465,463,363,188,93,21,77,373,5,182,379,87,27,172,78,64,12,358,167,472,466,456,364,189,94,22,374,6,183,380,80,28,173,65,79,13,359,160,473,467,457,365,190,95,23,375,7,176,381,81,29,174,451,452,453,455,448,449,450,454,875,866,865,864,876,850,842,844,851,847,846,845,852,848,843,890,891,892,889,888,644,778,755,697,729,723,713,761,681,788,666,745,650,675,772,794,660,691,739,645,779,756,698,730,724,714,762,682,789,667,746,651,676,773,795,661,692,740,646,780,757,699,731,725,715,763,683,790,668,747,652,677,774,796,662,693,741,647,781,758,700,732,726,716,764,684,791,669,748,653,678,775,797,663,694,742,641,782,759,701,733,727,717,765,685,784,670,749,654,679,768,798,656,695,743,640,783,752,702,734,720,718,766,686,785,671,769,750,655,672,736,799,657,688,770,776,642,753,703,735,721,719,767,687,786,664,751,648,673,737,792,658,689,777,771,643,754,696,728,722,712,760,680,787,665,744,649,674,738,793,659,690,706,707,708,710,711,704,705,709,815,812,813,810,819,827,824,825,826,823,816,820,822,809,814,817,808,821,818,811 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 = {6, 26, 46, 66, 86, 106, 127, 147, 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 2026-10-06 10:53:47 · history