Equation 677 Database

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Magma 1b2c5f1017c7…

magma 1b2c5f1017c7
Size
870
Isomorphism class hash
1b2c5f1017c74fb10107d90b098f76e07213727bcffab1abb7ef9f8caa2814f2
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 10:53:13
Display reorder
869,23,740,715,726,24,741,716,727,25,742,717,728,26,743,718,729,27,744,719,730,28,745,705,731,29,746,706,732,15,747,707,733,16,748,708,734,17,749,709,720,18,735,710,721,736,19,711,722,737,20,712,723,738,21,713,724,739,22,714,725,762,754,755,756,757,758,759,760,761,764,750,751,752,753,763,862,832,826,865,514,177,135,163,515,178,136,164,516,179,137,150,517,165,138,151,518,166,139,152,519,167,140,153,520,168,141,154,521,169,142,155,522,170,143,156,523,171,144,157,524,172,145,158,173,510,146,159,174,511,147,160,175,512,148,161,176,513,149,162,132,124,125,126,127,128,129,130,131,134,120,121,122,123,133,842,835,829,854,256,766,805,816,257,767,806,817,258,768,807,818,259,769,808,819,260,770,809,820,261,771,795,821,262,772,796,822,263,773,797,823,264,774,798,824,265,775,799,810,266,776,800,811,777,267,801,812,778,268,802,813,779,269,803,814,765,255,804,815,788,780,781,782,783,784,785,786,787,790,791,792,793,794,789,850,833,827,851,40,292,318,277,41,293,319,278,42,294,320,279,43,295,321,280,44,296,322,281,30,297,323,282,31,298,324,283,32,299,325,284,33,285,326,270,34,286,327,271,35,287,328,272,288,36,329,273,289,37,315,274,290,38,316,275,291,39,317,276,301,308,309,310,311,312,313,314,300,303,304,305,306,307,302,856,834,828,857,96,401,427,440,97,402,428,441,98,403,429,442,99,404,430,443,100,390,431,444,101,391,432,445,102,392,433,446,103,393,434,447,104,394,420,448,90,395,421,449,91,396,422,435,397,92,423,436,398,93,424,437,399,94,425,438,400,95,426,439,409,416,417,418,419,405,406,407,408,411,412,413,414,415,410,825,863,861,838,194,201,226,254,180,202,227,240,181,203,228,241,182,204,229,242,183,205,230,243,184,206,231,244,185,207,232,245,186,208,233,246,187,209,234,247,188,195,235,248,189,196,236,249,197,190,237,250,198,191,238,251,199,192,239,252,200,193,225,253,223,215,216,217,218,219,220,221,222,210,211,212,213,214,224,840,867,868,839,61,618,589,602,62,619,590,603,63,620,591,604,64,621,592,605,65,622,593,606,66,623,594,607,67,624,595,608,68,625,596,609,69,626,597,610,70,627,598,611,71,628,599,612,629,72,585,613,615,73,586,614,616,74,587,600,617,60,588,601,642,634,635,636,637,638,639,640,641,644,630,631,632,633,643,843,849,846,853,119,496,469,481,105,497,470,482,106,498,471,483,107,499,472,484,108,500,473,485,109,501,474,486,110,502,475,487,111,503,476,488,112,504,477,489,113,505,478,490,114,506,479,491,507,115,465,492,508,116,466,493,509,117,467,494,495,118,468,480,451,458,459,460,461,462,463,464,450,453,454,455,456,457,452,855,848,845,858,49,363,337,348,50,364,338,349,51,365,339,350,52,366,340,351,53,367,341,352,54,368,342,353,55,369,343,354,56,370,344,355,57,371,330,356,58,372,331,357,59,373,332,358,374,45,333,359,360,46,334,345,361,47,335,346,362,48,336,347,385,377,378,379,380,381,382,383,384,387,388,389,375,376,386,860,847,844,864,78,532,559,572,79,533,560,573,80,534,561,574,81,535,562,575,82,536,563,576,83,537,564,577,84,538,565,578,85,539,566,579,86,525,567,580,87,526,568,581,88,527,569,582,528,89,555,583,529,75,556,584,530,76,557,570,531,77,558,571,541,548,549,550,551,552,553,554,540,543,544,545,546,547,542,859,836,830,866,3,651,679,692,4,652,680,693,5,653,681,694,6,654,682,695,7,655,683,696,8,656,684,697,9,657,685,698,10,658,686,699,11,659,687,700,12,645,688,701,13,646,689,702,647,14,675,703,648,1,676,704,649,0,677,690,650,2,678,691,660,667,668,669,670,671,672,673,674,662,663,664,665,666,661,841,837,831,852 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#7c9587bb487c7f78877b32bd3c6516b6b04394ef6d405ed5492c6ed5480f025c, 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 10:53:15 · history