Equation 677 Database

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Magma 191d72e7b430…

magma 191d72e7b430
Size
870
Isomorphism class hash
191d72e7b4306a38a70e24aeb65f3d0c8efd353af821e28f050def4a11dcac2c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 869) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 18:34:36
Display reorder
869,750,775,780,243,751,776,781,244,752,777,782,245,753,778,783,246,754,779,784,247,755,765,785,248,756,766,786,249,757,767,787,250,758,768,788,251,759,769,789,252,760,770,790,253,761,771,791,254,762,772,792,240,763,773,793,241,764,774,794,242,796,803,804,805,806,807,808,809,795,798,799,800,801,802,797,862,832,826,865,522,530,550,59,523,531,551,45,524,532,552,46,510,533,553,47,511,534,554,48,512,535,540,49,513,536,541,50,514,537,542,51,515,538,543,52,516,539,544,53,517,525,545,54,518,526,546,55,519,527,547,56,520,528,548,57,521,529,549,58,565,557,558,559,560,561,562,563,564,567,568,569,555,556,566,842,835,829,854,274,298,305,816,275,299,306,817,276,285,307,818,277,286,308,819,278,287,309,820,279,288,310,821,280,289,311,822,281,290,312,823,282,291,313,824,283,292,314,810,284,293,300,811,270,294,301,812,271,295,302,813,272,296,303,814,273,297,304,815,256,263,264,265,266,267,268,269,255,258,259,260,261,262,257,850,833,827,851,64,88,93,318,65,89,94,319,66,75,95,320,67,76,96,321,68,77,97,322,69,78,98,323,70,79,99,324,71,80,100,325,72,81,101,326,73,82,102,327,74,83,103,328,60,84,104,329,61,85,90,315,62,86,91,316,63,87,92,317,108,115,116,117,118,119,105,106,107,110,111,112,113,114,109,856,834,828,857,443,403,409,127,444,404,410,128,445,390,411,129,446,391,412,130,447,392,413,131,448,393,414,132,449,394,415,133,435,395,416,134,436,396,417,120,437,397,418,121,438,398,419,122,439,399,405,123,440,400,406,124,441,401,407,125,442,402,408,126,424,431,432,433,434,420,421,422,423,426,427,428,429,430,425,825,863,861,838,175,183,204,236,176,184,205,237,177,185,206,238,178,186,207,239,179,187,208,225,165,188,209,226,166,189,195,227,167,190,196,228,168,191,197,229,169,192,198,230,170,193,199,231,171,194,200,232,172,180,201,233,173,181,202,234,174,182,203,235,218,210,211,212,213,214,215,216,217,220,221,222,223,224,219,840,867,868,839,631,655,660,13,632,656,661,14,633,657,662,1,634,658,663,0,635,659,664,2,636,645,665,3,637,646,666,4,638,647,667,5,639,648,668,6,640,649,669,7,641,650,670,8,642,651,671,9,643,652,672,10,644,653,673,11,630,654,674,12,675,682,683,684,685,686,687,688,689,677,678,679,680,681,676,843,849,846,853,493,502,461,148,494,503,462,149,480,504,463,135,481,505,464,136,482,506,450,137,483,507,451,138,484,508,452,139,485,509,453,140,486,495,454,141,487,496,455,142,488,497,456,143,489,498,457,144,490,499,458,145,491,500,459,146,492,501,460,147,475,467,468,469,470,471,472,473,474,477,478,479,465,466,476,855,848,845,858,382,330,351,29,383,331,352,15,384,332,353,16,385,333,354,17,386,334,355,18,387,335,356,19,388,336,357,20,389,337,358,21,375,338,359,22,376,339,345,23,377,340,346,24,378,341,347,25,379,342,348,26,380,343,349,27,381,344,350,28,365,372,373,374,360,361,362,363,364,367,368,369,370,371,366,860,847,844,864,604,627,570,164,605,628,571,150,606,629,572,151,607,615,573,152,608,616,574,153,609,617,575,154,610,618,576,155,611,619,577,156,612,620,578,157,613,621,579,158,614,622,580,159,600,623,581,160,601,624,582,161,602,625,583,162,603,626,584,163,585,592,593,594,595,596,597,598,599,587,588,589,590,591,586,859,836,830,866,696,705,727,44,697,706,728,30,698,707,729,31,699,708,730,32,700,709,731,33,701,710,732,34,702,711,733,35,703,712,734,36,704,713,720,37,690,714,721,38,691,715,722,39,692,716,723,40,693,717,724,41,694,718,725,42,695,719,726,43,743,735,736,737,738,739,740,741,742,745,746,747,748,749,744,841,837,831,852 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 870 = 1 + 11*79, 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, 11, B) with E = magma#98b16528073ac7b159dff157031893a3ff21fcc82cd65442bb1543925d4c715a, M = {75} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 79): MacNeish's product over GF(79); 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: 45.

last edited by qawbecrdtey at 2026-10-08 18:34:37 · history