Equation 677 Database

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Magma c8ec638efa88…

magma c8ec638efa88
Size
816
Isomorphism class hash
c8ec638efa88610120a656a6cd1a201d654698391220df716d4976618ae7f8de
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 815) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 10:25:56
Display reorder
549,550,536,537,538,539,540,541,542,543,544,545,546,547,548,765,354,589,419,637,287,53,446,41,79,80,355,590,420,638,288,54,447,42,81,356,591,421,639,289,55,448,43,357,82,578,422,640,290,56,449,44,78,358,579,423,736,679,667,687,665,701,702,704,703,722,291,57,450,31,83,359,580,424,628,292,58,451,32,84,360,581,425,629,293,45,452,33,85,361,582,426,630,294,46,453,34,86,362,583,427,631,295,47,454,35,87,363,584,428,632,296,48,455,36,88,364,585,429,633,297,49,456,37,89,351,586,430,634,298,50,457,38,90,352,587,431,635,299,51,458,39,91,353,588,432,636,300,52,459,40,215,211,212,213,214,739,759,750,710,760,751,752,749,709,740,767,770,771,766,774,772,775,768,769,773,312,258,507,520,337,528,558,472,494,495,729,678,693,695,683,696,697,688,691,715,259,508,521,338,529,559,460,301,496,260,509,522,326,530,560,461,497,302,261,510,523,327,531,561,462,485,303,249,498,511,328,532,562,463,486,304,250,499,512,329,734,698,689,690,680,677,692,694,682,720,563,464,487,305,251,500,513,330,533,551,465,488,306,252,501,514,331,534,552,466,489,307,253,502,515,332,535,553,467,490,308,254,503,516,333,524,554,468,491,309,255,504,517,334,525,555,469,492,310,256,505,518,335,526,556,470,493,311,257,506,519,336,527,557,471,218,225,226,227,228,229,230,216,217,220,221,222,223,224,219,800,798,797,803,805,809,811,808,810,807,387,568,156,178,396,187,147,72,595,596,388,569,157,179,397,188,148,73,597,389,570,158,180,398,189,149,74,390,598,571,159,181,399,190,150,75,599,391,572,160,182,400,191,151,76,600,392,573,161,169,401,192,152,77,601,379,574,162,170,402,193,153,64,602,380,575,163,171,403,194,154,65,603,381,576,164,172,404,195,141,66,604,382,577,165,173,405,196,142,67,735,685,699,672,673,686,674,671,668,721,383,564,166,174,406,183,143,68,592,384,565,167,175,393,184,144,69,593,385,566,168,176,394,185,145,70,594,386,567,155,177,395,186,146,71,62,63,59,60,61,737,758,746,705,757,745,747,748,706,738,812,814,815,806,813,780,782,785,776,778,664,663,348,412,484,0,16,279,444,445,743,744,730,731,733,725,726,728,732,764,763,716,717,719,708,707,714,724,718,723,624,625,626,620,619,280,433,641,642,349,413,473,116,105,281,434,644,643,350,414,474,117,106,282,435,646,645,339,415,475,118,107,283,436,648,647,340,416,476,119,108,284,437,650,649,341,417,477,120,109,285,438,652,651,342,418,478,121,110,286,439,654,653,343,407,479,122,111,274,440,656,655,344,408,480,123,112,275,441,658,657,345,409,481,124,113,276,442,660,659,346,410,482,125,114,277,443,662,661,347,411,483,126,115,278,9,2,1,3,4,5,6,7,8,11,12,13,14,15,10,787,791,789,793,795,802,799,804,796,801,365,131,21,319,236,98,267,610,202,203,366,132,22,320,237,99,268,611,204,367,133,23,321,238,100,269,612,368,205,134,24,322,239,101,270,613,206,369,135,25,323,240,102,271,614,207,370,136,26,324,241,103,272,615,208,371,137,27,325,242,104,273,616,209,372,138,17,313,243,92,727,700,675,684,670,666,681,676,669,713,617,210,373,139,28,623,621,618,622,627,197,374,140,29,314,231,93,262,605,198,375,127,30,315,232,94,263,606,199,376,128,18,316,233,95,264,607,200,377,129,19,317,234,96,265,608,201,378,130,20,318,235,97,266,609,248,244,245,246,247,741,761,753,712,762,754,755,756,711,742,777,781,784,779,783,790,794,788,786,792 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#a8d5635d8a1eab45f1aa212fea14621e2c1f3e6af2f9fc67d64ab2d160f5c6a2, M = {0, 10, 20, 32, 42, 52, 62, 72, 82, 92, 102, 112, 122, 132, 142, 168} 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 2026-10-08 10:25:57 · history