Equation 677 Database

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Magma 2ac486601acf…

magma 2ac486601acf
Size
705
Isomorphism class hash
2ac486601acf0d79b0369859576b74d3a22063fb55d1ebe89c9394158247eed3
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 19:44:27
Display reorder
660,575,590,305,592,41,576,591,593,303,39,574,589,594,304,40,586,578,595,301,44,587,579,596,302,42,588,577,597,300,43,581,598,311,573,47,582,599,309,571,45,580,600,310,572,46,601,584,307,569,50,602,585,308,570,48,583,603,306,568,49,687,688,686,685,146,343,179,142,212,144,344,143,177,210,145,342,141,178,211,346,149,138,175,215,347,147,139,176,213,345,148,140,174,214,341,133,170,152,207,339,134,168,150,208,340,132,169,151,209,136,337,173,155,206,137,338,171,153,204,336,135,172,154,205,703,704,701,702,553,566,299,522,535,554,567,520,297,536,555,565,521,298,537,562,552,525,295,534,563,550,523,296,532,564,551,524,294,533,557,528,290,544,541,558,526,288,545,542,556,527,289,546,543,531,560,293,547,540,529,561,291,548,538,559,530,292,549,539,671,672,670,669,233,241,358,15,224,231,242,16,359,222,232,240,17,357,223,244,229,18,354,227,245,230,19,355,225,243,228,20,356,226,247,21,349,239,219,248,22,350,237,220,246,23,348,238,221,24,250,352,235,218,25,251,353,236,216,249,26,351,234,217,679,680,678,677,405,370,31,374,387,406,371,372,32,388,407,369,373,30,389,366,404,377,27,386,367,402,375,28,384,368,403,376,29,385,361,380,37,396,393,362,378,38,397,394,360,379,36,398,395,383,364,33,399,392,381,365,34,400,390,363,382,35,401,391,692,691,690,689,272,464,61,473,481,270,462,471,62,482,271,463,472,60,480,467,275,469,57,484,465,273,470,58,485,466,274,468,59,483,459,479,52,267,487,460,477,53,268,488,461,478,51,269,486,475,458,55,266,490,476,456,56,264,491,457,474,54,265,489,699,700,698,697,89,96,7,109,80,87,97,110,8,78,88,98,108,6,79,99,85,112,10,83,100,86,113,11,81,101,84,111,9,82,102,115,5,95,75,103,116,3,93,76,104,114,4,94,77,118,105,0,91,74,119,106,2,92,72,107,117,1,90,73,663,664,662,661,638,642,321,606,619,639,640,604,322,620,637,641,605,323,621,645,634,609,320,618,643,635,607,318,616,644,636,608,319,617,648,612,312,629,625,646,610,313,630,626,647,611,314,628,627,615,651,315,632,624,613,649,316,633,622,650,614,317,631,623,682,683,684,681,14,512,282,64,500,12,513,65,283,501,13,511,63,284,499,510,503,502,285,498,654,653,652,286,655,659,658,657,287,656,518,67,280,506,493,519,68,281,504,494,517,66,279,505,492,70,514,276,509,496,71,515,277,507,497,516,69,278,508,495,695,696,693,694,425,433,255,449,409,423,434,447,256,410,424,432,448,257,408,436,421,445,254,412,437,422,446,252,413,435,420,444,253,411,439,455,261,431,415,440,453,262,429,416,438,454,263,430,414,451,442,260,427,418,452,443,258,428,419,441,450,259,426,417,667,668,665,666,188,195,335,157,120,186,196,158,333,121,187,197,156,334,122,194,191,160,331,123,192,189,161,332,124,193,190,159,330,125,201,163,326,183,126,202,164,324,184,127,203,162,325,185,128,166,200,329,182,129,167,198,327,180,130,199,165,328,181,131,675,676,673,674 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#a6f8f14c2d1a7a50e2f04288a5c27cfc248015f3a737479d1ca25990a259c6e6, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 19:44:28 · history