Equation 677 Database

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Magma f77ed813ea2d…

magma f77ed813ea2d
Size
705
Isomorphism class hash
f77ed813ea2d90654024a809e1709bacc1621de97112a740fe3e645ba4d16933
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 19:51:03
Display reorder
660,618,609,17,610,601,638,629,621,15,630,658,649,641,16,650,589,598,580,13,590,549,558,541,14,550,569,578,561,12,570,421,429,23,438,430,442,449,21,456,450,461,469,22,478,470,489,480,19,498,490,509,500,20,518,510,529,520,18,538,530,692,699,687,701,602,608,29,600,616,622,628,636,27,620,642,648,656,28,640,588,582,596,25,581,548,542,556,26,540,568,562,576,24,560,436,428,35,422,420,455,448,33,443,441,476,468,34,462,460,488,496,31,482,481,508,516,32,502,501,528,536,30,522,521,702,697,693,689,271,321,84,11,285,272,322,286,85,9,270,323,287,86,10,320,274,284,87,7,318,275,282,88,8,319,273,283,89,6,276,312,90,269,2,277,313,91,267,1,278,314,92,268,0,315,279,93,265,5,316,280,94,266,3,317,281,95,264,4,664,670,680,663,187,171,37,357,203,188,172,201,38,358,186,173,202,36,359,170,190,199,40,356,168,191,200,41,354,169,189,198,39,355,194,177,43,185,348,192,178,44,183,349,193,179,42,184,350,176,197,46,181,351,174,195,47,182,352,175,196,45,180,353,666,677,673,665,617,603,253,613,611,637,623,631,254,633,657,643,651,252,653,583,597,591,256,593,543,557,551,257,553,563,577,571,255,573,431,423,259,437,433,451,457,260,459,458,471,463,258,477,473,483,491,262,497,493,503,511,263,517,513,523,531,261,537,533,695,685,691,698,606,612,62,614,619,626,632,639,60,634,646,652,659,61,654,592,586,599,65,594,552,546,559,63,554,572,566,579,64,574,439,432,68,426,434,440,452,66,446,453,479,472,67,466,474,492,499,71,486,494,512,519,69,506,514,532,539,70,526,534,703,690,700,704,607,605,99,615,604,627,625,624,100,635,647,645,644,101,655,585,587,584,98,595,545,547,544,96,555,565,567,564,97,575,424,425,105,427,435,444,445,106,447,454,464,465,107,467,475,485,484,104,487,495,505,504,102,507,515,525,524,103,527,535,688,694,696,686,59,417,139,153,309,57,418,310,140,154,58,419,311,138,155,416,55,308,142,152,414,56,306,143,150,415,54,307,141,151,300,408,137,50,144,301,409,135,48,145,302,410,136,49,146,411,303,133,53,147,412,304,134,51,148,413,305,132,52,149,681,684,662,669,393,345,204,81,240,394,346,241,205,82,395,347,242,206,83,344,392,243,207,80,342,390,244,208,78,343,391,245,209,79,246,336,210,384,72,247,337,211,385,73,248,338,212,386,74,339,249,213,387,75,340,250,214,388,76,341,251,215,389,77,678,672,683,676,333,381,123,369,237,334,382,238,124,370,335,383,239,125,371,380,332,236,122,368,378,330,234,120,366,379,331,235,121,367,228,372,129,324,360,229,373,130,325,361,230,374,131,326,362,375,231,128,327,363,376,232,126,328,364,377,233,127,329,365,671,675,674,661,109,405,157,297,223,110,406,224,158,298,108,407,222,156,299,404,112,226,160,296,402,113,227,161,294,403,111,225,159,295,221,396,163,115,288,219,397,164,116,289,220,398,162,114,290,399,217,166,118,291,400,218,167,119,292,401,216,165,117,293,668,679,667,682 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#b24873ef385d9876d07add1b0ccd1e5b9965acff1b69e8225210d446f480d74b, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 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: 45.

last edited by qawbecrdtey at 2026-10-03 19:51:04 · history