Equation 677 Database

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Magma 59f1c5e14c56…

magma 59f1c5e14c56
Size
705
Isomorphism class hash
59f1c5e14c56e5ecd8097a9dbb5fa1ba9ba3aa859ab38518becb6a1c378cbba1
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 16:30:16
Display reorder
660,60,297,322,309,285,61,286,298,323,310,299,287,62,321,311,284,63,296,318,308,282,64,294,319,306,283,65,295,320,307,66,303,291,328,315,67,304,292,329,316,68,305,293,327,317,302,69,290,324,314,300,70,288,325,312,301,71,289,326,313,685,686,688,687,201,50,43,28,397,202,398,48,44,29,49,396,203,42,27,400,200,53,46,24,401,198,51,47,25,399,199,52,45,26,207,56,395,41,34,208,54,393,39,35,209,55,394,40,33,59,206,391,37,30,57,204,392,38,31,58,205,390,36,32,701,702,704,703,280,568,542,535,562,281,563,569,540,536,567,561,279,541,534,558,276,564,545,538,559,277,565,543,539,560,278,566,544,537,271,574,553,548,533,272,575,554,546,531,270,573,552,547,532,570,274,556,551,529,571,275,557,549,530,572,273,555,550,528,670,669,672,671,215,426,402,448,425,213,423,427,403,449,428,424,214,404,447,421,211,429,405,444,422,212,430,406,445,420,210,431,407,446,221,432,416,408,439,219,433,414,409,440,220,434,415,410,438,435,217,419,411,442,436,218,417,412,443,437,216,418,413,441,680,677,679,678,224,457,114,14,194,222,192,458,115,12,456,193,223,116,13,197,227,460,117,17,195,225,461,118,15,196,226,459,119,16,230,455,189,112,20,228,453,190,113,18,229,454,191,111,19,451,233,188,108,23,452,231,186,109,21,450,232,187,110,22,689,690,691,692,8,171,247,518,159,6,160,172,248,516,173,161,7,246,517,158,11,170,250,521,156,9,168,251,519,157,10,169,249,520,3,177,165,253,513,4,178,166,254,514,5,179,167,252,515,176,2,164,256,512,174,1,162,257,510,175,0,163,255,511,697,698,700,699,579,609,635,612,593,580,591,610,633,613,611,592,581,634,614,589,578,608,631,615,590,576,606,632,616,588,577,607,630,617,585,600,599,626,618,586,601,597,624,619,587,602,598,625,620,603,584,595,629,621,604,582,596,627,622,605,583,594,628,623,661,662,664,663,95,137,338,77,126,93,127,135,336,75,136,128,94,337,76,129,91,133,341,73,130,92,134,339,74,131,90,132,340,72,86,143,124,333,83,84,141,125,334,81,85,142,123,335,82,139,89,120,332,79,140,87,121,330,80,138,88,122,331,78,682,681,684,683,101,261,524,180,266,99,264,262,522,181,263,265,100,523,182,269,97,260,527,183,267,98,258,525,184,268,96,259,526,185,107,642,640,643,641,105,646,644,647,645,106,636,637,638,639,654,103,653,655,652,658,104,656,659,657,650,102,649,651,648,693,694,696,695,235,468,495,479,500,236,498,469,496,477,470,499,234,497,478,503,238,471,494,475,501,239,472,492,476,502,237,473,493,474,241,466,506,486,485,242,467,504,487,483,240,465,505,488,484,462,244,509,489,481,463,245,507,490,482,464,243,508,491,480,666,665,668,667,150,379,354,353,377,151,375,380,355,351,378,376,152,356,352,373,153,382,357,349,374,154,383,358,350,372,155,381,359,348,148,385,368,360,344,149,386,366,361,342,147,384,367,362,343,388,144,371,363,347,389,145,369,364,345,387,146,370,365,346,674,673,676,675 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#34588157c307db5531c4fa8d738de6f4f43dd6ced943a299dd02fbb5d9b36bf1, 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 16:30:17 · history