Equation 677 Database

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Magma f0c3ed73490b…

magma f0c3ed73490b
Size
876
Isomorphism class hash
f0c3ed73490bba3f8b6d422f4b1d5a6d3ebe430ebd368eaa233ae82da777a829
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 18:32:31
Display reorder
855,501,489,662,639,666,667,448,21,390,12,665,502,490,663,640,669,670,449,22,391,668,13,491,503,664,641,672,673,450,23,392,671,14,492,504,652,642,675,676,437,24,393,674,11,493,505,653,643,678,677,679,438,25,394,8,494,506,654,644,681,680,682,439,26,395,9,495,655,507,645,684,683,685,440,27,396,10,508,496,656,646,687,686,688,441,16,397,7,509,497,657,647,690,689,691,442,17,398,4,510,498,658,648,692,693,694,443,18,386,5,511,499,659,649,695,696,697,444,19,387,6,512,500,660,650,698,699,700,445,20,388,3,488,513,661,651,701,702,703,446,784,801,783,817,815,814,816,704,705,706,447,15,389,2,818,819,821,820,823,822,824,741,743,746,735,834,860,857,863,858,856,861,862,838,859,383,277,154,85,518,261,545,546,421,180,572,384,278,155,86,519,262,547,548,422,573,181,279,385,156,87,520,263,549,550,423,574,170,280,373,144,88,521,264,551,552,412,575,171,281,374,145,89,522,576,265,553,554,413,172,282,375,146,90,523,577,266,555,556,414,173,283,147,376,91,524,578,267,557,558,415,174,377,284,148,92,525,579,0,559,560,416,175,378,285,149,80,526,580,596,600,601,417,176,379,286,150,81,514,581,603,611,612,418,177,380,287,151,82,515,582,615,623,624,419,178,381,288,152,83,516,570,627,635,636,420,179,289,382,153,84,517,571,260,544,732,727,714,712,726,718,709,807,812,794,810,811,803,790,769,774,760,755,779,782,767,742,749,747,736,874,872,871,825,837,847,826,828,844,848,366,335,209,45,63,229,401,106,463,302,536,367,336,210,46,64,230,402,107,464,537,303,337,368,211,47,65,231,403,108,465,538,304,338,369,212,48,66,232,404,109,466,539,305,330,370,213,49,54,540,233,405,110,467,306,331,371,214,50,55,541,221,406,111,468,307,332,215,372,51,56,542,222,407,112,469,308,360,333,216,52,57,543,223,408,113,470,1,361,334,217,53,58,599,224,409,114,471,591,362,592,218,41,59,610,225,410,115,472,605,363,607,219,42,60,622,226,411,116,473,617,364,619,220,43,61,634,227,399,117,474,629,631,365,208,44,62,535,228,400,710,729,720,716,725,722,708,785,809,792,802,788,806,797,771,773,764,752,753,780,765,740,757,777,738,866,869,870,827,831,851,842,832,845,843,188,345,476,40,79,199,310,527,583,451,428,189,346,477,28,67,200,311,528,584,429,452,347,190,478,29,68,201,312,529,585,430,453,348,191,479,30,69,202,313,530,586,431,454,349,192,480,31,70,432,203,314,531,587,455,350,193,481,32,71,433,204,315,532,588,456,351,482,194,33,72,434,205,316,533,589,457,182,339,483,34,73,435,206,317,534,590,458,183,340,484,35,74,436,207,597,598,602,459,184,341,485,36,75,424,195,606,609,614,460,185,342,486,37,76,425,196,618,621,626,461,186,343,487,38,77,426,197,630,633,638,462,344,187,475,39,78,427,198,309,731,734,728,730,715,723,707,786,804,791,798,808,813,805,772,762,778,751,754,775,763,770,748,750,776,864,868,875,852,840,841,849,830,839,850,163,561,133,238,120,97,257,290,318,358,269,164,562,134,239,121,98,258,291,319,270,359,563,165,135,240,122,99,259,292,320,271,352,564,166,136,241,123,100,247,293,321,272,353,565,167,137,242,124,273,101,248,294,322,354,566,168,138,243,125,274,102,249,295,323,355,567,139,169,244,126,275,103,250,296,324,356,157,568,140,245,127,276,104,251,297,325,357,158,569,141,246,128,595,105,252,298,326,593,159,594,142,234,129,604,93,253,299,327,608,160,613,143,235,130,616,94,254,300,328,620,161,625,131,236,118,628,95,255,301,329,632,637,162,132,237,119,268,96,256,719,721,724,711,713,733,717,789,795,787,793,796,799,800,781,761,759,766,758,768,756,737,744,745,739,867,873,865,846,854,835,833,829,836,853 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#cfc7e4bc59b22006f60ebd7ce77473023ab55d49dc5fdde77a5095697b261f2e, 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 18:32:33 · history