Equation 677 Database

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Magma 5a0ff53e4321…

magma 5a0ff53e4321
Size
705
Isomorphism class hash
5a0ff53e432187986c7fb2f03ecb290dbaf2f605cb46e628d5d46c2e0e340d54
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 21:21:26
Display reorder
660,577,259,584,566,12,585,257,575,567,13,576,586,568,258,14,587,573,255,569,15,588,574,256,570,16,589,572,254,571,17,583,564,590,265,18,581,565,591,263,19,582,563,592,264,20,560,579,593,261,21,561,580,594,262,22,562,578,595,260,23,687,688,686,685,314,393,336,307,296,337,394,315,305,297,316,335,306,392,298,332,317,396,303,299,333,318,397,304,300,334,319,395,302,301,320,313,327,391,294,321,311,328,389,295,322,312,326,390,293,309,323,330,387,290,310,324,331,388,291,308,325,329,386,292,703,704,701,702,242,5,544,235,550,542,3,243,233,548,244,543,234,4,549,547,245,0,231,553,545,246,2,232,551,546,247,1,230,552,248,241,539,11,556,249,239,540,9,554,250,240,541,10,555,237,251,538,7,559,238,252,536,8,557,236,253,537,6,558,671,672,670,669,175,401,119,163,158,117,402,176,164,156,174,118,162,403,157,115,178,400,166,161,116,179,398,167,159,114,177,399,165,160,181,169,110,407,153,182,170,108,408,154,180,168,109,409,155,172,184,113,406,152,173,185,111,404,150,171,183,112,405,151,679,680,678,677,427,193,435,419,448,436,194,425,420,446,426,434,421,192,447,438,423,196,418,451,439,424,197,416,449,437,422,195,417,450,433,410,441,191,454,431,411,442,189,452,432,412,440,190,453,413,429,444,187,457,414,430,445,188,455,415,428,443,186,456,692,691,690,689,514,126,219,35,135,220,127,512,33,136,513,221,34,128,137,218,517,129,31,134,216,515,130,32,132,217,516,131,30,133,509,26,210,124,141,510,24,211,125,142,511,25,212,123,143,29,508,213,120,140,27,506,214,121,138,28,507,215,122,139,699,700,698,697,58,46,70,94,82,71,47,59,95,83,57,69,93,45,81,66,54,42,90,78,67,55,43,91,79,68,56,44,92,80,49,85,61,37,73,50,86,62,38,74,48,84,60,36,72,88,52,64,40,76,89,53,65,41,77,87,51,63,39,75,663,664,662,661,634,273,596,625,617,597,274,632,623,618,633,598,624,272,619,599,637,276,621,616,600,635,277,622,614,601,636,275,620,615,640,631,602,271,608,638,629,603,269,609,639,630,604,270,610,627,643,605,267,611,628,641,606,268,612,626,642,607,266,613,682,683,684,681,659,106,658,657,656,650,107,651,648,649,655,654,652,105,653,525,529,102,527,223,644,646,103,645,647,524,528,104,526,222,531,146,523,97,227,532,144,521,98,228,530,145,522,96,229,149,534,519,100,226,147,535,520,101,224,148,533,518,99,225,695,696,693,694,473,204,491,467,497,492,205,474,468,498,475,493,469,206,499,490,472,207,466,496,488,470,208,464,494,489,471,209,465,495,479,458,482,202,503,480,459,483,203,504,481,460,484,201,505,461,478,485,198,502,462,476,486,199,500,463,477,487,200,501,667,668,665,666,351,280,363,339,376,364,278,352,340,374,350,362,338,279,375,366,354,283,342,379,367,355,281,343,377,365,353,282,341,378,357,345,369,286,382,358,346,370,284,380,356,344,368,285,381,348,360,372,289,385,349,361,373,287,383,347,359,371,288,384,675,676,673,674 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#eb741fb6db55479c3e56ca4f84f09a48d9f1cbf15ed347cc0747015cb842acab, 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 21:21:27 · history