Equation 677 Database

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Magma 2f4084e5a637…

magma 2f4084e5a637
Size
870
Isomorphism class hash
2f4084e5a637a1a0ec7d825b3570f86c52ee93beef1f37f8ff781fea62359562
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
2026-10-06 08:20:16
Display reorder
869,344,441,434,414,330,442,420,415,331,443,421,416,332,444,422,417,333,445,423,418,334,446,424,419,335,447,425,405,336,448,426,406,337,449,427,407,338,435,428,408,339,436,429,409,340,437,430,410,341,438,431,411,342,439,432,412,413,440,343,433,464,456,457,458,459,460,461,462,463,451,452,453,454,455,450,847,828,829,837,29,216,209,243,15,217,195,244,16,218,196,245,17,219,197,246,18,220,198,247,19,221,199,248,20,222,200,249,21,223,201,250,22,224,202,251,23,210,203,252,24,211,204,253,25,212,205,254,26,213,206,240,27,214,207,241,242,215,28,208,225,232,233,234,235,236,237,238,239,227,228,229,230,231,226,848,842,846,838,74,128,106,100,60,129,107,101,61,130,108,102,62,131,109,103,63,132,110,104,64,133,111,90,65,134,112,91,66,120,113,92,67,121,114,93,68,122,115,94,69,123,116,95,70,124,117,96,71,125,118,97,72,126,119,98,99,127,73,105,83,75,76,77,78,79,80,81,82,85,86,87,88,89,84,835,834,831,830,317,387,366,346,318,388,367,347,319,389,368,348,320,375,369,349,321,376,370,350,322,377,371,351,323,378,372,352,324,379,373,353,325,380,374,354,326,381,360,355,327,382,361,356,328,383,362,357,329,384,363,358,315,385,364,359,345,386,316,365,396,403,404,390,391,392,393,394,395,398,399,400,401,402,397,836,843,844,827,9,635,629,607,10,636,615,608,11,637,616,609,12,638,617,610,13,639,618,611,14,640,619,612,1,641,620,613,0,642,621,614,2,643,622,600,3,644,623,601,4,630,624,602,5,631,625,603,6,632,626,604,7,633,627,605,606,634,8,628,658,650,651,652,653,654,655,656,657,645,646,647,648,649,659,859,861,856,853,675,756,736,730,676,757,737,731,677,758,738,732,678,759,739,733,679,760,740,734,680,761,741,720,681,762,742,721,682,763,743,722,683,764,744,723,684,750,745,724,685,751,746,725,686,752,747,726,687,753,748,727,688,754,749,728,729,755,689,735,711,718,719,705,706,707,708,709,710,713,714,715,716,717,712,864,841,845,858,59,171,164,142,45,172,150,143,46,173,151,144,47,174,152,145,48,175,153,146,49,176,154,147,50,177,155,148,51,178,156,149,52,179,157,135,53,165,158,136,54,166,159,137,55,167,160,138,56,168,161,139,57,169,162,140,141,170,58,163,194,186,187,188,189,190,191,192,193,181,182,183,184,185,180,850,833,832,839,539,519,499,493,525,520,500,494,526,521,501,480,527,522,502,481,528,523,503,482,529,524,504,483,530,510,505,484,531,511,506,485,532,512,507,486,533,513,508,487,534,514,509,488,535,515,495,489,536,516,496,490,537,517,497,491,492,518,538,498,475,467,468,469,470,471,472,473,474,477,478,479,465,466,476,851,868,867,852,39,298,278,256,40,299,279,257,41,285,280,258,42,286,281,259,43,287,282,260,44,288,283,261,30,289,284,262,31,290,270,263,32,291,271,264,33,292,272,265,34,293,273,266,35,294,274,267,36,295,275,268,37,296,276,269,255,297,38,277,307,314,300,301,302,303,304,305,306,309,310,311,312,313,308,863,865,866,854,660,561,541,588,661,562,542,589,662,563,543,590,663,564,544,591,664,565,545,592,665,566,546,593,666,567,547,594,667,568,548,595,668,569,549,596,669,555,550,597,670,556,551,598,671,557,552,599,672,558,553,585,673,559,554,586,587,560,674,540,571,578,579,580,581,582,583,584,570,573,574,575,576,577,572,862,840,849,857,699,815,808,787,700,816,809,788,701,817,795,789,702,818,796,790,703,819,797,791,704,820,798,792,690,821,799,793,691,822,800,794,692,823,801,780,693,824,802,781,694,810,803,782,695,811,804,783,696,812,805,784,697,813,806,785,786,814,698,807,770,777,778,779,765,766,767,768,769,772,773,774,775,776,771,860,825,826,855 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#9916b9303e5777c051d457f13e65b220048127e3f9475b765d37bfd24fd4df83, M = {75} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 2026-10-06 08:20:21 · history