Equation 677 Database

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Magma cdb3e2bc6550…

magma cdb3e2bc6550
Size
876
Isomorphism class hash
cdb3e2bc655056f30370bdf267387d49d5375b1a82c30f5539355409fc18517b
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 826 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 21:14:54
Display reorder
853,339,652,40,639,666,665,93,343,209,367,667,340,653,41,640,669,668,94,344,210,670,355,341,654,42,641,672,671,95,345,211,673,356,329,655,43,642,675,346,96,674,212,676,357,330,656,44,643,678,679,97,677,347,213,358,331,657,45,644,681,682,98,348,680,214,359,658,332,46,645,684,685,683,349,215,99,360,659,333,47,646,687,688,686,100,350,203,361,660,334,48,647,690,691,689,101,351,204,362,661,335,36,648,693,694,692,88,352,205,363,662,336,37,649,696,697,695,89,353,206,364,663,337,38,650,699,700,698,90,354,207,365,664,338,39,651,702,703,701,91,800,793,801,817,815,814,816,705,706,704,92,342,208,366,821,819,818,820,822,824,823,736,749,747,740,857,863,859,856,855,862,861,858,854,860,85,615,498,64,550,286,445,8,159,228,394,86,617,499,65,551,287,446,9,160,395,229,87,619,500,66,552,288,447,10,161,396,230,75,621,501,67,553,11,448,289,162,397,231,76,623,502,68,554,398,449,290,3,163,232,77,625,503,69,555,399,450,4,278,164,233,627,78,504,70,556,400,279,5,153,451,234,629,79,505,71,557,401,280,452,6,154,235,631,80,506,72,558,402,281,453,7,155,236,633,81,507,73,559,403,282,454,0,156,237,635,82,508,74,560,404,283,455,1,157,238,637,83,509,62,561,405,284,456,2,158,239,613,84,497,63,549,406,285,457,707,714,718,734,711,727,710,811,804,798,807,783,790,795,781,753,773,752,777,766,762,742,743,745,739,864,865,871,835,845,839,829,849,834,851,316,198,576,601,616,151,381,268,433,216,114,317,199,577,602,618,152,382,269,434,102,217,318,200,578,603,620,140,383,270,435,103,218,319,201,579,604,622,271,384,141,436,104,219,320,202,580,605,624,105,385,142,272,437,220,321,190,581,606,626,106,386,273,143,438,221,191,322,582,607,628,107,144,274,439,387,222,192,323,583,608,630,108,145,388,275,440,223,193,324,584,609,632,109,146,389,276,441,224,194,325,585,610,634,110,147,390,277,442,225,195,326,586,611,636,111,148,391,266,443,226,196,327,587,612,638,112,149,392,267,444,227,197,328,575,600,614,113,150,393,720,725,717,716,723,731,733,813,787,789,803,797,806,794,758,764,779,780,782,754,757,741,761,769,738,867,866,870,841,827,844,833,825,847,826,134,537,524,291,511,458,248,165,589,121,417,135,538,525,292,512,459,249,166,590,418,122,136,539,526,293,513,460,250,167,591,419,123,137,540,527,294,514,168,251,461,592,407,124,138,541,528,295,515,408,252,462,169,593,125,139,542,529,296,516,409,240,170,463,594,126,543,127,530,297,517,410,464,171,595,241,115,544,128,531,298,518,411,465,242,172,596,116,545,129,532,299,519,412,466,243,173,597,117,546,130,533,300,520,413,467,244,174,598,118,547,131,534,301,521,414,468,245,175,599,119,548,132,535,302,522,415,469,246,176,588,120,536,133,523,303,510,416,470,247,715,732,712,729,713,728,721,810,805,808,796,791,812,788,776,756,775,763,774,767,770,759,746,750,755,873,875,869,846,852,850,840,831,832,828,563,426,253,472,485,49,178,304,23,31,376,564,427,254,473,486,50,179,305,12,377,32,565,428,255,474,487,51,180,306,13,378,33,566,429,256,475,488,307,181,52,14,379,34,567,430,257,476,489,380,182,53,308,15,35,568,431,258,477,490,368,183,309,54,16,24,432,569,259,478,491,369,55,310,17,184,25,420,570,260,479,492,370,56,185,311,18,26,421,571,261,480,493,371,57,186,312,19,27,422,572,262,481,494,372,58,187,313,20,28,423,573,263,482,495,373,59,188,314,21,29,424,574,264,483,496,374,60,189,315,22,30,425,562,265,471,484,375,61,177,722,708,709,724,730,719,726,809,802,786,792,799,784,785,768,778,760,771,772,765,751,737,748,744,735,868,874,872,842,836,843,837,830,848,838 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 876 = 1 + 5*175, 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#e8ca3c576bc15e850b7516f6d3462538705335e939b0822293437654d0eb3162, M = {165} 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, 175): MacNeish's product over GF(25) x GF(7); GF(25) = F_5[x]/(x^2 + 2); 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: 51.

last edited by qawbecrdtey at 2026-10-07 21:14:55 · history