Equation 677 Database

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Magma 9566dbb9fe3e…

magma 9566dbb9fe3e
Size
876
Isomorphism class hash
9566dbb9fe3eb0b72985a5062c71c105d3631a8c3fdac3c80188f8ecdeeadf90
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
2026-10-06 18:51:32
Display reorder
857,6,619,238,610,665,666,628,586,660,659,667,7,620,239,611,668,669,629,587,662,670,661,8,621,240,599,672,671,630,588,664,673,663,9,622,241,600,675,674,631,589,649,676,640,10,623,229,601,678,679,677,632,590,650,641,624,11,230,602,681,682,591,633,680,651,642,612,12,231,603,684,685,683,634,592,652,643,613,0,232,604,687,688,635,686,593,653,644,614,1,233,605,690,691,689,636,594,654,645,615,2,234,606,693,694,692,637,595,655,646,616,3,235,607,696,697,695,638,596,656,647,617,4,236,608,699,700,698,625,597,657,648,618,5,237,609,702,703,701,626,811,813,812,817,814,815,816,705,706,704,627,598,658,639,821,818,819,820,822,824,823,741,749,750,742,862,856,858,855,825,859,863,860,854,861,538,255,339,459,119,243,65,130,550,485,417,539,256,340,460,120,244,66,131,551,418,486,540,257,341,461,121,245,67,132,552,419,487,541,258,342,462,122,246,68,133,553,407,488,542,259,343,463,123,408,247,69,134,554,489,260,543,331,464,124,409,135,70,248,555,490,261,544,332,465,125,410,249,71,136,556,491,262,545,333,466,126,411,72,250,137,557,492,263,546,334,467,127,412,251,73,138,558,493,264,547,335,468,128,413,252,74,139,559,494,265,548,336,469,129,414,253,75,140,560,495,266,536,337,470,117,415,254,76,141,549,496,267,537,338,471,118,416,242,77,710,732,729,716,731,720,727,788,803,796,785,789,809,806,764,781,768,776,758,773,763,735,743,747,740,868,869,873,842,835,840,836,846,841,830,319,180,394,382,91,526,281,357,142,164,455,320,181,395,383,92,527,282,358,143,456,165,321,182,396,384,93,528,283,359,144,457,154,322,183,397,385,94,529,284,360,145,458,155,323,184,398,386,95,446,530,285,361,146,156,185,324,399,387,96,447,362,286,531,147,157,186,325,400,388,97,448,532,287,363,148,158,187,326,401,389,98,449,288,533,364,149,159,188,327,402,390,99,450,534,289,365,150,160,189,328,403,391,100,451,535,290,366,151,161,190,329,404,392,101,452,523,291,367,152,162,191,330,405,393,102,453,524,292,368,153,163,179,318,406,381,103,454,525,280,722,711,712,713,719,725,724,787,805,808,798,801,790,791,761,767,772,771,756,775,780,738,770,759,736,870,864,874,848,829,834,849,850,828,827,344,506,104,424,306,19,222,193,370,293,53,345,507,105,425,307,20,223,194,371,54,294,346,508,106,426,308,21,224,195,372,55,295,347,509,107,427,309,22,225,196,373,56,296,348,497,108,428,310,57,23,226,197,374,297,498,349,109,429,311,58,198,227,24,375,298,499,350,110,430,312,59,25,228,199,376,299,500,351,111,431,313,60,216,13,200,377,300,501,352,112,432,314,61,14,217,201,378,301,502,353,113,420,315,62,15,218,202,379,302,503,354,114,421,316,63,16,219,203,380,303,504,355,115,422,317,64,17,220,192,369,304,505,356,116,423,305,52,18,221,714,723,718,730,721,709,726,800,784,783,795,793,802,799,778,769,757,774,766,754,751,762,744,746,765,865,867,871,851,853,832,833,852,847,831,473,563,34,39,167,78,436,576,212,269,514,474,564,35,40,168,79,437,577,213,515,270,475,565,36,41,169,80,438,578,214,516,271,476,566,37,42,170,81,439,579,215,517,272,477,567,38,43,171,518,82,440,580,204,273,568,478,27,44,172,519,581,441,83,205,274,569,479,28,45,173,520,84,442,582,206,275,570,480,29,46,174,521,443,85,583,207,276,571,481,30,47,175,522,86,444,584,208,277,572,482,31,48,176,510,87,445,585,209,278,573,483,32,49,177,511,88,433,574,210,279,561,484,33,50,178,512,89,434,575,211,268,562,472,26,51,166,513,90,435,734,715,717,733,728,707,708,792,807,786,804,810,794,797,782,777,752,753,760,779,755,739,748,745,737,875,872,866,837,843,838,844,839,826,845 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#401be786137dc36f5d100cc07f6618b2bbcf4bdd3efbb07f53dbc44f3de0d8c7, 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 2026-10-06 18:51:34 · history