Equation 677 Database

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Magma 835e07dd2168…

magma 835e07dd2168
Size
816
Isomorphism class hash
835e07dd2168b788df1bd7619f47a81f204652825278ed022aeaa67b83a5fcf7
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 766 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 15:25:47
Display reorder
560,561,562,563,564,565,566,567,568,569,570,571,572,573,764,815,74,220,38,233,172,239,246,112,287,282,709,717,706,718,715,720,719,712,724,725,350,368,347,370,360,395,396,385,401,403,351,369,348,371,361,394,397,386,402,404,75,219,39,232,283,173,238,247,113,288,596,639,585,641,655,623,643,645,608,657,597,690,586,691,693,689,692,646,606,658,67,491,31,492,494,490,493,248,105,289,68,501,32,502,504,500,503,240,106,290,69,511,33,512,514,510,513,241,107,291,70,521,34,522,524,520,523,242,108,292,71,531,35,532,534,530,533,243,109,284,72,541,36,542,544,540,543,244,110,285,73,551,37,552,554,550,553,245,111,286,598,695,584,696,698,697,694,644,607,656,806,807,779,781,780,805,804,778,808,782,373,363,353,358,355,380,381,399,378,392,295,179,92,162,132,52,43,271,204,22,296,180,93,154,133,44,53,272,205,23,660,625,602,617,612,588,591,652,634,581,297,181,94,155,206,125,45,54,273,24,298,182,95,156,207,126,46,55,274,25,661,626,600,618,635,610,589,592,653,582,299,174,87,157,208,127,47,56,275,26,300,175,88,158,209,128,48,57,276,27,374,362,352,357,366,387,379,382,400,377,301,176,89,159,201,129,40,49,277,28,659,624,601,619,633,611,587,590,651,583,293,177,90,160,202,130,41,50,269,29,294,178,91,161,203,131,42,51,270,30,726,756,711,754,758,750,753,707,723,705,814,803,789,788,777,813,812,787,811,786,420,469,424,465,468,467,421,422,423,466,729,743,733,739,742,730,741,731,740,732,425,474,429,470,473,472,426,427,471,428,430,479,434,475,478,477,431,432,476,433,435,484,439,480,481,483,482,436,437,438,440,489,444,485,486,488,487,441,442,443,734,748,738,744,745,747,746,735,736,737,445,499,449,496,495,498,497,446,447,448,450,509,454,505,506,508,507,451,452,453,455,519,459,515,516,518,517,456,457,458,460,529,464,525,526,528,527,461,462,463,406,539,409,535,536,538,537,405,407,408,410,549,414,545,546,548,547,411,412,413,415,559,419,555,556,558,557,416,417,418,684,703,688,699,700,701,702,685,686,687,791,790,769,765,766,794,793,768,792,767,314,310,313,312,118,231,148,252,81,311,319,315,318,317,119,149,221,253,316,82,324,320,323,322,120,222,150,254,321,83,329,325,328,327,121,223,151,255,326,84,334,330,333,332,331,122,224,152,256,85,339,336,338,337,335,123,225,153,257,86,683,679,682,681,680,666,670,668,672,665,344,340,343,342,341,124,226,143,258,76,678,675,677,676,674,667,671,669,673,664,302,234,303,278,12,114,227,144,259,77,662,642,663,654,577,609,640,616,647,599,304,235,305,279,10,115,228,145,249,78,306,236,307,280,11,116,229,146,250,79,308,237,309,281,9,117,230,147,251,80,727,762,728,763,761,760,752,714,721,710,798,799,774,773,772,797,796,771,795,770,575,580,615,628,620,638,595,632,650,605,1,17,140,183,163,65,218,193,100,261,2,18,141,184,164,210,66,194,101,262,3,19,142,185,165,211,58,195,102,263,4,20,134,186,103,166,212,59,196,264,5,21,135,187,104,167,213,60,197,265,375,376,388,390,384,359,367,349,365,372,345,346,356,364,354,389,393,383,391,398,6,13,136,188,96,168,214,61,198,266,7,14,137,189,97,169,215,62,199,267,8,15,138,190,98,170,216,63,200,268,0,16,139,191,99,171,217,64,192,260,576,579,613,629,603,621,636,593,630,648,574,578,614,627,604,622,637,594,631,649,704,749,713,757,751,759,755,708,716,722,810,809,785,783,784,800,801,775,802,776 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 816 = 16 + 5*160, 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, 5, B) with E = magma#6a399a9c87e7071f82c2b558a15c305208ee5447d6f1dcb94d7a1b560bd62e8a, M = {0, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133, 144, 155, 166} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 160): MacNeish's product over GF(32) x GF(5); GF(32) = F_2[x]/(x^5 + x^2 + 1); 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: 51.

last edited by qawbecrdtey at 2026-10-07 15:25:48 · history