Equation 677 Database

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Magma fb1de9dc751e…

magma fb1de9dc751e
Size
705
Isomorphism class hash
fb1de9dc751e4cc09fcec63a5a5451590ef51894ca94fe4e3487148c9069c923
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 19:57:30
Display reorder
660,133,335,626,633,330,134,336,627,634,331,135,337,628,632,329,334,132,629,636,326,332,130,630,637,327,333,131,631,635,328,139,341,624,639,321,140,342,625,640,322,141,343,623,638,320,340,138,620,642,324,338,136,621,643,325,339,137,622,641,323,687,688,686,685,417,189,211,217,226,418,190,212,218,227,416,191,210,216,225,192,420,207,213,229,193,421,208,214,230,194,419,209,215,228,423,195,202,223,232,424,196,203,224,233,422,197,201,222,231,198,426,205,219,235,199,427,206,220,236,200,425,204,221,234,703,704,701,702,311,128,590,596,619,312,129,591,597,617,313,127,592,598,618,124,310,593,599,615,125,308,594,600,616,126,309,595,601,614,317,119,588,602,610,318,120,589,603,608,319,118,587,604,609,122,316,584,605,613,123,314,585,606,611,121,315,586,607,612,671,672,670,669,175,436,443,452,240,176,434,444,453,241,174,435,445,454,242,439,171,442,455,239,437,172,440,456,237,438,173,441,457,238,166,431,449,458,246,167,432,450,459,247,165,433,451,460,248,430,169,448,461,245,428,170,446,462,243,429,168,447,463,244,679,680,678,677,469,255,261,187,80,467,256,262,188,78,468,257,263,186,79,258,465,264,183,83,259,466,265,184,81,260,464,266,185,82,475,253,267,178,86,473,254,268,179,84,474,252,269,177,85,249,471,270,181,89,250,472,271,182,87,251,470,272,180,88,692,691,690,689,288,529,546,552,562,289,527,547,553,560,290,528,545,551,561,525,287,542,548,565,526,285,543,549,563,524,286,544,550,564,294,535,537,558,568,295,533,538,559,566,296,534,536,557,567,531,293,540,554,571,532,291,541,555,569,530,292,539,556,570,699,700,698,697,7,27,50,57,67,8,28,48,58,68,6,29,49,59,66,26,10,53,56,70,24,11,51,54,71,25,9,52,55,69,13,18,45,63,73,14,19,46,64,74,12,20,47,65,72,21,16,44,62,76,22,17,42,60,77,23,15,43,61,75,663,664,662,661,646,357,99,150,350,644,358,100,148,351,645,356,101,149,352,360,649,98,153,353,361,647,96,151,354,359,648,97,152,355,652,363,90,145,348,650,364,91,146,349,651,362,92,147,347,366,655,93,144,344,367,653,94,142,345,365,654,95,143,346,682,683,684,681,573,115,109,305,155,574,116,110,303,156,572,117,108,304,154,114,576,112,307,158,657,577,656,658,659,113,575,111,306,157,579,2,107,300,161,580,1,105,301,159,578,0,106,302,160,5,582,103,299,164,3,583,104,297,162,4,581,102,298,163,695,696,693,694,284,501,523,487,492,282,502,521,485,493,283,500,522,486,491,504,280,519,483,488,505,281,520,484,489,503,279,518,482,490,275,507,514,478,498,273,508,512,476,499,274,506,513,477,497,510,278,517,481,494,511,276,515,479,495,509,277,516,480,496,667,668,665,666,35,402,409,376,385,33,403,407,374,383,34,401,408,375,384,398,31,405,379,381,399,32,406,377,382,400,30,404,378,380,41,393,415,371,391,39,394,413,372,389,40,392,414,373,390,396,37,411,370,387,397,38,412,368,388,395,36,410,369,386,675,676,673,674 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#b82bea23d952545bcb5d6b6a0cc235694bb3bc5cc3b3a153b6c38e307d02b955, 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 19:57:31 · history