Equation 677 Database

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Magma 85ede5fa1238…

magma 85ede5fa1238
Size
870
Isomorphism class hash
85ede5fa1238d20abaa38f0a83a9061ee4826631f68e17b03f94f8cc6d27c6f6
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 20:12:52
Display reorder
869,333,358,379,452,453,334,359,380,454,335,345,381,455,336,346,382,456,337,347,383,457,338,348,384,458,339,349,385,459,340,350,386,341,460,351,387,352,461,342,388,353,462,343,389,354,463,344,375,464,355,330,376,450,356,331,377,451,357,332,378,360,367,368,369,370,371,372,373,374,362,363,364,365,366,361,847,828,829,837,99,108,75,132,133,100,109,76,134,101,110,77,120,102,111,78,121,103,112,79,122,104,113,80,123,90,114,81,124,91,115,82,92,125,116,83,117,126,93,84,118,127,94,85,119,128,95,86,129,105,96,87,130,106,97,88,131,107,98,89,73,65,66,67,68,69,70,71,72,60,61,62,63,64,74,848,842,846,838,228,252,219,25,26,229,253,220,27,230,254,221,28,231,240,222,29,232,241,223,15,233,242,224,16,234,243,210,17,235,244,211,236,18,245,212,246,19,237,213,247,20,238,214,248,21,239,215,22,249,225,216,23,250,226,217,24,251,227,218,268,260,261,262,263,264,265,266,267,255,256,257,258,259,269,835,834,831,830,407,432,398,8,9,408,433,399,10,409,434,400,11,410,420,401,12,411,421,402,13,412,422,403,14,413,423,404,1,414,424,390,415,0,425,391,426,2,416,392,427,3,417,393,428,4,418,394,5,429,419,395,6,430,405,396,7,431,406,397,448,440,441,442,443,444,445,446,447,435,436,437,438,439,449,836,843,844,827,596,605,571,33,34,597,606,572,35,598,607,573,36,599,608,574,37,585,609,575,38,586,610,576,39,587,611,577,40,588,612,578,589,41,613,579,614,42,590,580,600,43,591,581,601,44,592,582,30,602,593,583,31,603,594,584,32,604,595,570,568,560,561,562,563,564,565,566,567,555,556,557,558,559,569,859,861,856,853,777,788,751,681,682,778,789,752,683,779,790,753,684,765,791,754,685,766,792,755,686,767,793,756,687,768,794,757,688,769,780,758,770,689,781,759,782,675,771,760,783,676,772,761,784,677,773,762,678,785,774,763,679,786,775,764,680,787,776,750,806,798,799,800,801,802,803,804,805,808,809,795,796,797,807,864,841,845,858,280,289,322,196,197,281,290,323,198,282,291,324,199,283,292,325,200,284,293,326,201,270,294,327,202,271,295,328,203,272,296,329,273,204,297,315,298,205,274,316,299,206,275,317,285,207,276,318,208,286,277,319,209,287,278,320,195,288,279,321,305,312,313,314,300,301,302,303,304,307,308,309,310,311,306,850,833,832,839,526,483,516,474,475,527,484,517,476,528,485,518,477,529,486,519,478,530,487,520,479,531,488,521,465,532,489,522,466,533,490,523,534,467,491,524,492,468,535,510,493,469,536,511,494,470,537,512,471,480,538,513,472,481,539,514,473,482,525,515,499,506,507,508,509,495,496,497,498,501,502,503,504,505,500,851,868,867,852,183,138,174,46,47,184,139,175,48,185,140,176,49,186,141,177,50,187,142,178,51,188,143,179,52,189,144,165,53,190,145,166,191,54,146,167,147,55,192,168,148,56,193,169,149,57,194,170,58,135,180,171,59,136,181,172,45,137,182,173,155,162,163,164,150,151,152,153,154,157,158,159,160,161,156,863,865,866,854,618,643,665,540,541,619,644,666,542,620,630,667,543,621,631,668,544,622,632,669,545,623,633,670,546,624,634,671,547,625,635,672,626,548,636,673,637,549,627,674,638,550,628,660,639,551,629,661,552,640,615,662,553,641,616,663,554,642,617,664,646,653,654,655,656,657,658,659,645,648,649,650,651,652,647,862,840,849,857,717,728,691,815,816,718,729,692,817,719,730,693,818,705,731,694,819,706,732,695,820,707,733,696,821,708,734,697,822,709,720,698,710,823,721,699,722,824,711,700,723,810,712,701,724,811,713,702,812,725,714,703,813,726,715,704,814,727,716,690,745,737,738,739,740,741,742,743,744,747,748,749,735,736,746,860,825,826,855 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#8622272f99ed7258e0e5c3e0e3c3c55307035c123d24328e2a163f5e0fb74bfb, 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 2026-10-08 20:12:53 · history