Equation 677 Database

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Magma ccffc40eb884…

magma ccffc40eb884
Size
816
Isomorphism class hash
ccffc40eb8843dd40bada986f3adc4c5eee0de01e5d5bfb4f2847cd964e48644
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
2026-10-06 08:20:35
Display reorder
560,561,562,563,564,565,566,567,568,569,570,571,572,573,764,815,126,201,248,268,271,44,119,154,260,121,715,721,723,714,725,726,707,713,718,724,386,395,398,384,400,372,349,360,363,370,387,396,399,385,401,373,350,361,364,371,127,193,247,122,272,270,36,120,153,269,648,651,654,652,653,631,643,620,610,645,649,693,586,689,612,632,692,691,690,646,494,261,37,490,128,194,493,492,491,253,504,262,38,500,129,195,503,502,501,254,514,263,39,510,130,196,513,512,511,255,524,264,40,520,131,197,523,522,521,256,534,265,41,530,123,198,533,532,531,257,544,266,42,540,124,199,543,542,541,258,554,267,43,550,125,200,553,552,551,259,695,611,633,697,650,698,587,694,696,647,780,802,779,803,772,806,782,804,805,781,392,382,391,389,403,354,355,351,357,367,178,94,171,213,143,282,70,76,46,88,179,95,172,214,135,283,71,77,47,89,626,604,623,635,614,658,594,598,588,600,180,96,173,215,284,136,63,78,48,81,137,64,285,79,181,97,174,49,216,82,615,659,595,599,627,605,624,589,636,601,286,138,65,80,182,98,166,50,217,83,287,139,66,72,183,90,167,51,218,84,404,388,380,381,393,358,365,352,368,356,288,140,67,73,175,91,168,52,219,85,660,616,596,597,625,603,622,590,637,602,289,141,68,74,176,92,169,53,220,86,290,142,69,75,177,93,170,45,221,87,756,720,711,753,716,759,709,751,750,710,787,810,786,811,771,814,789,812,813,788,421,424,468,423,466,422,465,467,420,469,730,733,742,743,732,740,731,739,741,729,426,429,473,474,428,471,427,470,472,425,431,434,478,479,433,476,432,475,477,430,436,439,483,484,481,438,437,480,482,435,443,442,486,485,441,444,488,487,489,440,737,745,736,744,735,738,747,746,748,734,495,448,447,496,446,449,498,497,499,445,506,453,452,505,451,454,508,507,509,450,516,458,457,515,456,459,518,517,519,455,526,463,462,525,461,464,528,527,529,460,536,408,407,535,405,409,538,537,539,406,546,413,412,545,411,414,548,547,549,410,556,418,417,555,416,419,558,557,559,415,703,685,688,702,687,700,686,699,701,684,768,792,767,791,766,793,765,794,790,769,160,314,312,246,212,113,294,310,313,311,161,319,317,316,236,202,114,295,315,318,162,324,322,321,237,203,115,296,320,323,163,329,327,326,238,204,116,297,325,328,164,334,332,331,205,239,117,298,330,333,240,118,206,299,165,339,337,336,335,338,670,668,664,672,667,683,681,679,680,682,207,241,108,300,155,344,342,340,341,343,669,671,665,673,666,678,676,675,674,677,208,242,109,301,156,303,249,235,231,302,634,642,609,661,621,663,644,613,641,662,209,243,110,291,157,305,250,132,232,304,210,244,111,292,158,307,251,133,233,306,211,245,112,293,159,309,252,134,234,308,762,719,728,763,722,755,712,760,761,727,778,801,777,799,775,797,776,798,800,774,593,583,655,617,608,577,582,630,576,638,58,27,273,222,144,100,9,19,192,3,59,28,274,223,145,101,10,20,184,4,60,29,275,224,146,102,11,21,185,5,61,30,276,225,103,147,12,22,186,6,148,13,104,23,62,31,277,187,226,7,362,359,346,347,353,378,402,394,397,375,383,390,376,377,379,348,374,366,369,345,105,149,14,24,54,32,278,188,227,8,106,150,15,25,55,33,279,189,228,0,107,151,16,26,56,34,280,190,229,1,99,152,17,18,57,35,281,191,230,2,606,618,578,581,591,584,656,628,639,575,607,619,579,580,592,585,657,629,640,574,757,708,706,758,717,752,705,749,754,704,784,807,783,795,773,809,770,796,808,785 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#a3828220131148cef6b96d6f643589aa4db41a9cb4e92ffb50ae89a2fa6e00cc, M = {0, 11, 22, 33, 45, 59, 70, 81, 93, 104, 115, 126, 137, 148, 155, 165} 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 2026-10-06 08:20:36 · history