Equation 677 Database

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Magma e094716f4da0…

magma e094716f4da0
Size
816
Isomorphism class hash
e094716f4da091d7f413fa39f79533ad392fc2e5d18c79390b8950a288ea334e
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 12:21:15
Display reorder
458,461,462,463,464,465,466,467,468,469,470,456,457,460,459,765,556,557,577,576,560,561,594,593,589,590,764,763,761,762,751,750,742,743,747,746,542,548,568,562,543,549,569,563,544,550,570,564,545,551,571,565,546,552,572,566,547,553,573,567,541,554,574,0,575,555,729,732,730,731,734,733,686,688,687,685,693,690,692,691,689,698,695,697,696,694,483,31,452,234,18,484,32,453,235,19,485,33,454,236,20,486,34,455,237,21,487,35,444,238,22,488,24,445,239,23,489,25,446,240,15,490,26,447,241,16,491,27,448,242,17,492,28,449,243,14,493,29,450,244,13,494,558,559,579,578,30,451,245,12,495,105,112,98,99,100,101,102,103,104,107,108,109,110,111,106,767,766,769,770,768,774,773,775,772,771,424,186,267,340,427,189,270,343,428,190,271,344,429,191,272,345,430,192,273,346,431,193,274,347,432,194,275,336,420,195,669,672,679,651,670,673,680,650,671,674,421,183,276,337,422,184,277,338,339,423,185,266,426,188,269,342,61,179,230,138,596,619,648,657,641,595,620,649,658,642,1,62,180,231,139,2,63,181,232,140,3,64,182,233,141,4,65,172,223,131,5,66,173,224,132,6,67,174,225,133,7,68,175,226,134,8,69,176,227,135,597,621,646,655,639,598,622,647,656,640,9,70,177,228,136,10,425,187,268,341,71,178,229,137,11,261,262,263,264,265,666,667,668,659,661,662,663,664,665,660,815,813,812,814,811,780,779,778,777,776,374,387,400,313,377,390,592,591,585,586,758,752,756,757,749,748,738,739,745,744,378,391,402,305,379,392,403,306,380,393,404,307,381,394,405,308,382,395,406,309,383,396,407,310,384,397,398,311,312,385,386,399,376,389,581,580,588,583,584,587,754,760,753,755,759,735,741,736,737,740,285,476,315,328,413,286,477,316,329,414,287,478,317,330,415,288,479,318,331,416,289,480,319,332,417,281,481,320,333,418,282,482,321,334,419,283,471,322,335,408,284,472,323,324,409,280,473,143,325,410,279,474,144,326,411,278,375,388,401,314,475,142,327,412,582,298,290,291,292,293,294,295,296,297,300,301,302,303,304,299,808,806,810,807,809,804,803,801,802,805,254,359,213,162,257,362,216,165,258,363,217,166,259,364,218,167,260,365,219,168,246,366,220,169,247,367,221,170,248,368,222,171,249,369,208,157,250,370,209,158,251,371,210,159,252,372,211,160,161,253,373,212,256,361,215,164,517,519,520,518,699,700,702,703,701,704,705,707,708,706,521,522,524,525,523,526,527,529,530,528,709,710,712,713,711,714,715,717,718,716,531,532,534,535,533,536,537,539,540,538,719,720,722,723,721,724,725,727,728,726,497,496,499,500,498,505,501,503,504,502,506,507,509,510,508,511,255,360,214,163,512,514,515,513,516,130,126,127,128,129,635,636,637,638,630,631,632,633,634,629,785,782,783,784,781,789,788,787,786,790,675,681,652,614,677,683,654,616,678,684,200,40,350,436,201,41,351,437,202,42,352,438,203,43,353,439,204,44,354,440,205,45,355,441,206,46,356,442,207,47,357,443,196,36,358,433,197,37,38,348,434,198,349,435,199,39,89,52,75,115,145,90,53,76,116,146,91,54,77,117,147,92,55,78,118,148,93,56,79,119,149,94,57,80,120,150,95,58,81,121,151,96,59,82,122,152,97,60,83,123,153,85,48,84,124,154,86,49,72,125,155,87,50,73,113,156,88,51,74,114,643,625,617,623,627,644,676,682,653,615,626,618,624,628,645,602,609,610,611,612,613,599,600,601,604,605,606,607,608,603,795,791,794,792,793,796,797,799,800,798 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#99cb45b67a2dc9ee437518638e58d067aa46b7acbabf3a3a9e16b3d48cee22eb, M = {0, 5, 10, 15, 20, 25, 31, 36, 41, 46, 50, 55, 62, 65, 140, 171} 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 12:21:16 · history