Equation 677 Database

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Magma f2e853b2abf0…

magma f2e853b2abf0
Size
765
Isomorphism class hash
f2e853b2abf037dece02426cc8b50b93d3c2a70b647b753bbee1790484b15ebc
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 764) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 16:46:35
Display reorder
301,279,103,67,90,302,280,104,68,91,303,281,105,69,92,304,282,106,70,93,297,275,107,63,94,298,276,108,64,95,299,277,101,65,88,300,278,102,66,89,705,706,685,680,689,127,85,42,341,138,166,215,74,37,362,141,242,57,328,174,121,86,43,342,139,164,216,75,38,363,142,254,58,329,175,122,87,44,337,140,165,563,520,506,608,538,582,515,598,551,533,525,508,600,536,548,564,521,507,358,143,246,59,324,176,123,81,39,338,135,163,212,71,34,359,144,247,60,325,177,124,82,40,339,136,433,213,72,35,245,360,145,178,61,326,243,125,83,41,340,137,434,214,73,36,361,146,179,62,327,126,244,84,509,601,535,625,565,522,505,607,537,550,514,597,501,502,665,503,504,664,670,671,759,758,757,760,755,761,756,688,683,702,715,690,695,681,710,691,640,641,636,644,646,613,611,635,642,556,578,547,570,561,532,604,616,586,427,312,383,370,186,412,197,240,157,223,208,115,349,402,260,0,313,384,371,187,413,198,241,158,224,209,116,350,403,261,2,311,385,372,188,414,557,579,545,571,562,531,605,617,587,490,594,612,610,553,618,558,580,546,225,210,117,351,404,262,3,310,386,373,162,415,159,199,237,118,226,211,160,456,457,454,452,455,387,374,453,458,195,238,119,221,206,464,161,465,460,467,470,388,375,459,466,196,239,120,222,207,478,482,486,479,483,487,676,677,732,740,741,737,736,739,734,713,718,693,696,701,687,700,698,763,170,131,288,283,425,271,249,436,314,447,293,333,148,97,306,171,132,289,284,426,272,250,437,315,448,294,334,149,98,307,172,133,290,285,424,273,251,438,316,449,295,335,150,99,308,173,134,291,286,422,274,252,439,317,450,296,336,151,100,309,167,128,33,287,423,269,253,440,1,451,292,330,540,526,591,549,534,629,628,630,589,583,633,631,599,634,632,592,541,527,331,168,129,462,461,468,270,248,469,471,472,463,305,147,96,169,332,130,638,637,643,590,581,645,647,648,639,593,539,528,621,622,669,623,620,668,674,675,753,747,752,751,742,748,743,722,724,711,727,723,707,721,726,725,568,576,543,615,626,555,495,500,513,511,497,493,530,603,560,569,577,544,400,428,193,14,30,56,47,15,7,114,348,205,220,236,156,401,429,194,9,31,51,48,16,8,109,343,200,217,233,152,396,430,189,10,32,52,49,17,4,110,344,201,218,234,153,397,431,190,11,27,53,50,18,5,111,345,202,219,235,154,398,432,191,12,28,54,6,45,19,203,112,346,491,566,574,542,614,624,554,494,499,512,510,496,559,529,602,567,492,575,155,399,435,192,13,29,55,46,20,204,113,347,481,485,488,480,484,489,679,678,729,738,735,733,728,730,731,699,703,684,694,682,697,686,712,764,409,380,231,183,367,444,474,79,258,416,25,394,320,267,354,410,381,232,184,368,445,473,80,259,417,26,395,321,268,355,411,382,227,185,369,446,663,650,585,660,651,658,596,654,655,659,657,572,652,656,661,662,523,653,418,21,389,322,263,356,405,376,228,180,364,441,476,76,255,419,22,390,323,264,357,406,377,229,181,365,442,477,77,256,391,420,23,352,318,265,392,407,378,230,182,366,443,475,78,257,421,24,353,319,266,408,393,379,573,552,609,627,649,524,584,619,498,606,595,588,517,518,667,519,516,666,672,673,749,744,750,754,762,746,745,719,716,717,720,708,714,709,704,692 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 765 = 45 + 5*144, 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#28c135c31c9c16f63ac84541dde3ead566850ad6b588a124a02a031b47e5c71c, M = the submagma generated by {0, 6} (45 elements) 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, 144): MacNeish's product over GF(16) x GF(9); GF(16) = F_2[x]/(x^4 + x + 1), GF(9) = F_3[x]/(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: 85.

last edited by qawbecrdtey at 2026-10-07 16:46:36 · history