Equation 677 Database

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Magma a6300746d65e…

magma a6300746d65e
Size
705
Isomorphism class hash
a6300746d65e946f3b5c87a13d6f0470373a56a975ec89cae24ab6b108b22316
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 20:45:42
Display reorder
660,356,168,341,352,369,169,339,353,354,370,340,170,351,355,371,171,337,348,359,368,172,338,349,357,366,173,336,350,358,367,174,332,343,362,375,175,330,344,360,376,176,331,342,361,377,335,177,346,365,374,333,178,347,363,372,334,179,345,364,373,685,686,688,687,461,102,476,444,472,103,474,445,459,473,475,104,446,460,471,105,479,447,457,468,106,477,448,458,469,107,478,449,456,470,100,482,442,452,463,101,480,443,450,464,99,481,441,451,462,485,96,438,455,466,483,97,439,453,467,484,98,440,454,465,701,702,704,703,329,163,611,312,594,164,609,313,327,595,610,162,314,328,596,166,607,315,325,597,167,608,316,326,598,165,606,317,324,599,161,602,310,320,592,159,600,311,318,593,160,601,309,319,591,605,157,306,323,588,603,158,307,321,589,604,156,308,322,590,670,669,672,671,494,67,114,5,230,68,115,3,492,228,116,66,4,493,229,70,117,0,497,233,71,118,2,495,231,69,119,1,496,232,65,112,11,489,236,63,113,9,490,234,64,111,10,491,235,108,61,7,488,239,109,62,8,486,237,110,60,6,487,238,680,677,679,678,520,247,34,504,12,248,35,505,521,13,33,246,506,519,14,250,30,507,516,15,251,31,508,517,16,249,32,509,518,17,245,25,502,511,18,243,26,503,512,19,244,24,501,510,20,28,241,498,514,21,29,242,499,515,22,27,240,500,513,23,689,690,691,692,292,204,274,278,578,205,275,276,293,576,273,206,277,291,577,207,270,281,288,581,208,271,279,289,579,209,272,280,290,580,210,265,284,298,573,211,266,282,299,574,212,264,283,297,575,268,213,287,294,572,269,214,285,295,570,267,215,286,296,571,697,698,700,699,52,78,635,44,618,79,633,42,53,619,634,80,43,51,620,81,631,47,48,621,82,632,45,49,622,83,630,46,50,623,76,626,39,58,616,77,624,40,59,617,75,625,41,57,615,629,72,38,54,612,627,73,36,55,613,628,74,37,56,614,661,662,664,663,401,137,123,384,185,135,124,385,399,183,125,136,386,400,184,133,122,387,397,181,134,120,388,398,182,132,121,389,396,180,143,129,382,392,191,141,130,383,390,189,142,131,381,391,190,128,139,378,395,187,126,140,379,393,188,127,138,380,394,186,682,681,684,683,584,151,301,224,221,152,302,222,582,219,300,150,223,583,220,154,304,227,587,217,155,305,225,585,218,153,303,226,586,216,149,642,640,643,641,147,644,646,647,645,148,637,636,638,639,654,145,653,655,652,658,146,656,659,657,650,144,649,651,648,693,694,696,695,532,258,555,560,534,259,556,558,533,535,557,260,559,531,536,261,554,563,528,537,262,552,561,529,538,263,553,562,530,539,256,546,566,523,540,257,547,564,524,541,255,548,565,522,542,549,252,569,526,543,550,253,567,527,544,551,254,568,525,545,666,665,668,667,410,85,427,203,418,86,428,201,408,419,426,84,202,409,417,88,430,199,413,414,89,431,200,411,415,87,429,198,412,416,91,433,194,405,424,92,434,192,406,425,90,432,193,407,423,436,94,197,404,420,437,95,195,402,421,435,93,196,403,422,674,673,676,675 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#d368fcffc98defb742f81d5388b25ae4c38c7de7079297526f4ed93fca5d0bec, 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 20:45:43 · history