Equation 677 Database

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Magma 4ee055e9a8f9…

magma 4ee055e9a8f9
Size
870
Isomorphism class hash
4ee055e9a8f96908ea9138f53512e84eb7eee12f872c3c801d4ad0cc6bb61113
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
2026-10-07 15:20:16
Display reorder
869,748,295,718,760,749,296,719,761,735,297,705,762,736,298,706,763,737,299,707,764,738,285,708,750,739,286,709,751,740,287,710,752,741,288,711,753,742,289,712,754,743,290,713,755,744,291,714,756,745,292,715,757,293,746,716,758,294,747,717,759,731,723,724,725,726,727,728,729,730,733,734,720,721,722,732,862,832,826,865,551,58,519,562,552,59,520,563,553,45,521,564,554,46,522,565,540,47,523,566,541,48,524,567,542,49,510,568,543,50,511,569,544,51,512,555,545,52,513,556,546,53,514,557,547,54,515,558,548,55,516,559,56,549,517,560,57,550,518,561,532,539,525,526,527,528,529,530,531,534,535,536,537,538,533,842,835,829,854,805,301,774,816,806,302,775,817,807,303,776,818,808,304,777,819,809,305,778,820,795,306,779,821,796,307,765,822,797,308,766,823,798,309,767,824,799,310,768,810,800,311,769,811,801,312,770,812,802,313,771,813,314,803,772,814,300,804,773,815,787,794,780,781,782,783,784,785,786,789,790,791,792,793,788,850,833,827,851,369,148,338,329,370,149,339,315,371,135,340,316,372,136,341,317,373,137,342,318,374,138,343,319,360,139,344,320,361,140,330,321,362,141,331,322,363,142,332,323,364,143,333,324,365,144,334,325,366,145,335,326,146,367,336,327,147,368,337,328,352,359,345,346,347,348,349,350,351,354,355,356,357,358,353,856,834,828,857,205,439,174,151,206,440,175,152,207,441,176,153,208,442,177,154,209,443,178,155,195,444,179,156,196,445,165,157,197,446,166,158,198,447,167,159,199,448,168,160,200,449,169,161,201,435,170,162,202,436,171,163,437,203,172,164,438,204,173,150,187,194,180,181,182,183,184,185,186,189,190,191,192,193,188,825,863,861,838,79,60,114,90,80,61,115,91,81,62,116,92,82,63,117,93,83,64,118,94,84,65,119,95,85,66,105,96,86,67,106,97,87,68,107,98,88,69,108,99,89,70,109,100,75,71,110,101,76,72,111,102,73,77,112,103,74,78,113,104,127,134,120,121,122,123,124,125,126,129,130,131,132,133,128,840,867,868,839,226,633,262,253,227,634,263,254,228,635,264,240,229,636,265,241,230,637,266,242,231,638,267,243,232,639,268,244,233,640,269,245,234,641,255,246,235,642,256,247,236,643,257,248,237,644,258,249,238,630,259,250,631,239,260,251,632,225,261,252,275,282,283,284,270,271,272,273,274,277,278,279,280,281,276,843,849,846,853,469,37,505,480,470,38,506,481,471,39,507,482,472,40,508,483,473,41,509,484,474,42,495,485,475,43,496,486,476,44,497,487,477,30,498,488,478,31,499,489,479,32,500,490,465,33,501,491,466,34,502,492,35,467,503,493,36,468,504,494,452,459,460,461,462,463,464,450,451,454,455,456,457,458,453,855,848,845,858,407,13,375,434,408,14,376,420,409,1,377,421,410,0,378,422,411,2,379,423,412,3,380,424,413,4,381,425,414,5,382,426,415,6,383,427,416,7,384,428,417,8,385,429,418,9,386,430,419,10,387,431,11,405,388,432,12,406,389,433,403,395,396,397,398,399,400,401,402,390,391,392,393,394,404,860,847,844,864,607,222,575,618,608,223,576,619,609,224,577,620,610,210,578,621,611,211,579,622,612,212,580,623,613,213,581,624,614,214,582,625,600,215,583,626,601,216,584,627,602,217,570,628,603,218,571,629,604,219,572,615,220,605,573,616,221,606,574,617,589,596,597,598,599,585,586,587,588,591,592,593,594,595,590,859,836,830,866,646,26,680,672,647,27,681,673,648,28,682,674,649,29,683,660,650,15,684,661,651,16,685,662,652,17,686,663,653,18,687,664,654,19,688,665,655,20,689,666,656,21,675,667,657,22,676,668,658,23,677,669,24,659,678,670,25,645,679,671,695,702,703,704,690,691,692,693,694,697,698,699,700,701,696,841,837,831,852 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#6b9c8d3036868a08370ad1878f562fe0c41374f2f554fb65dddd9aba27979bde, 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 2026-10-07 15:20:18 · history