Equation 677 Database

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Magma 54d8fdc109bf…

magma 54d8fdc109bf
Size
909
Isomorphism class hash
54d8fdc109bf5df33f56a75dab659bd804b91619a41a90102df32098e518e393
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 15:53:58
Display reorder
807,801,800,802,803,804,805,806,908,292,368,495,162,314,481,361,184,308,497,383,178,447,417,431,359,511,298,168,293,369,488,163,315,482,362,185,309,498,376,179,440,418,424,353,504,299,169,294,370,489,164,316,483,363,186,310,499,377,180,441,419,425,352,505,300,170,295,371,490,165,317,484,364,187,311,500,378,181,442,420,426,354,506,301,171,288,372,491,166,318,485,365,188,304,501,379,182,443,421,427,355,507,302,172,289,373,492,167,319,486,366,189,305,502,380,183,444,422,428,173,356,508,303,374,290,493,160,312,487,367,190,306,503,381,176,445,423,429,174,357,509,296,375,291,494,161,313,480,360,191,307,496,382,177,446,416,430,175,358,510,297,432,433,434,436,437,438,439,435,858,875,865,874,879,836,828,844,835,829,840,845,832,833,831,886,887,883,885,884,415,207,112,449,399,126,223,479,385,96,193,465,10,26,20,209,110,401,463,408,200,113,450,392,127,216,472,386,97,194,466,11,27,21,210,111,402,456,409,201,114,451,393,120,217,473,387,98,195,467,12,28,22,211,104,403,457,410,202,115,452,394,121,218,474,388,99,196,468,13,29,23,212,105,404,458,411,203,116,453,395,122,219,475,389,100,197,469,14,30,16,213,106,405,459,412,204,117,454,396,123,220,476,390,101,198,470,15,31,17,460,214,107,406,205,413,118,455,397,124,221,477,391,102,199,471,8,24,18,461,215,108,407,206,414,119,448,398,125,222,478,384,103,192,464,9,25,19,462,208,109,400,3,4,5,7,1,0,2,6,876,862,859,864,867,860,878,866,861,877,863,868,871,873,872,834,837,841,830,839,634,611,518,624,586,521,571,582,560,536,617,552,229,245,251,549,535,615,614,635,613,519,625,587,520,572,583,561,537,618,553,230,246,252,550,534,610,609,636,608,513,626,588,522,573,576,562,538,619,554,231,247,253,551,528,602,597,637,594,512,627,589,523,574,577,563,539,620,555,224,240,254,545,529,603,598,638,595,514,628,590,524,575,578,564,540,621,556,225,241,255,544,530,604,599,639,596,515,629,591,525,569,579,565,541,622,557,226,242,248,600,546,531,605,593,632,516,630,584,526,568,580,566,542,623,558,227,243,249,601,547,532,606,592,633,517,631,585,527,570,581,567,543,616,559,228,244,250,612,548,533,607,234,235,236,238,239,232,233,237,855,854,857,853,856,897,905,906,907,902,893,895,901,899,900,894,903,896,904,898,263,134,344,94,285,338,150,78,279,328,140,64,63,33,47,156,322,269,80,256,135,345,95,286,339,151,79,272,329,141,65,56,34,40,157,323,270,81,257,128,346,88,287,340,144,72,273,330,142,66,57,35,41,158,324,271,82,258,129,347,89,280,341,145,73,274,331,143,67,58,36,42,159,325,264,83,259,130,348,90,281,342,146,74,275,332,136,68,59,37,43,152,326,265,84,260,131,349,91,282,343,147,75,276,333,137,69,60,38,44,85,153,327,266,132,261,350,92,283,336,148,76,277,334,138,70,61,39,45,86,154,320,267,133,262,351,93,284,337,149,77,278,335,139,71,62,32,46,87,155,321,268,48,49,50,52,53,54,55,51,881,869,882,870,880,850,849,847,852,848,838,846,842,843,851,888,890,891,892,889,683,799,745,725,693,743,775,709,699,752,784,715,661,651,645,777,767,677,731,684,792,746,726,694,737,769,710,700,753,785,716,662,652,646,778,760,678,732,685,793,747,727,695,736,768,711,701,754,786,717,663,653,647,779,761,679,733,686,794,748,720,688,738,770,704,702,755,787,718,656,654,641,780,762,672,734,687,795,749,721,689,739,771,705,703,756,788,719,657,655,640,781,763,673,735,680,796,750,722,690,740,772,706,696,757,789,712,658,648,642,728,782,764,674,797,681,751,723,691,741,773,707,697,758,790,713,659,649,643,729,783,765,675,798,682,744,724,692,742,774,708,698,759,791,714,660,650,644,730,776,766,676,666,667,668,670,671,664,665,669,821,808,817,810,820,824,827,825,823,826,811,819,815,813,814,809,818,822,816,812 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 = {15, 35, 55, 75, 95, 112, 120, 141, 181} 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 15:53:59 · history