Equation 677 Database

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Magma 6dddc2bda921…

magma 6dddc2bda921
Size
705
Isomorphism class hash
6dddc2bda9217e1d4b4cf7ccbd919b8b22052356e4e934fcf03d962b7a49fd62
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 17:24:09
Display reorder
660,282,594,292,604,100,283,293,605,595,101,284,596,291,603,99,597,285,288,600,96,598,286,289,601,97,599,287,290,602,98,298,592,610,280,106,299,593,611,281,107,297,591,609,279,105,588,294,606,276,102,589,295,607,277,103,590,296,608,278,104,687,688,686,685,31,51,366,36,377,32,367,37,52,375,30,53,368,38,376,50,34,369,39,373,48,35,370,40,374,49,33,371,41,372,364,57,42,29,383,365,58,43,27,381,363,59,44,28,382,56,360,45,25,379,54,361,46,26,380,55,362,47,24,378,703,704,701,702,6,547,568,552,578,7,569,553,548,576,8,546,567,554,577,550,9,564,555,581,551,10,565,556,579,549,11,566,557,580,574,545,558,4,584,575,543,559,5,582,573,544,560,3,583,541,570,561,1,587,542,571,562,0,585,540,572,563,2,586,671,672,670,669,21,421,400,384,410,22,401,385,422,408,23,420,399,386,409,424,20,396,387,413,425,18,397,388,411,423,19,398,389,412,406,427,390,12,416,407,428,391,13,414,405,426,392,14,415,430,402,393,15,419,431,403,394,16,417,429,404,395,17,418,679,680,678,677,204,445,90,465,439,205,91,466,446,440,206,444,92,467,438,448,207,93,464,442,449,208,94,462,443,447,209,95,463,441,88,451,456,210,437,89,452,457,211,435,87,450,458,212,436,454,84,459,213,433,455,85,460,214,434,453,86,461,215,432,692,691,690,689,516,273,250,238,262,517,251,239,274,263,518,275,249,237,261,272,519,246,234,258,270,520,247,235,259,271,521,248,236,260,241,264,229,522,253,242,265,230,523,254,240,266,228,524,252,267,244,232,525,256,268,245,233,526,257,269,243,231,527,255,699,700,698,697,144,172,197,180,159,145,195,181,173,160,146,171,196,182,161,168,147,193,183,158,169,148,194,184,156,170,149,192,185,157,203,178,186,150,165,201,179,187,151,166,202,177,188,152,167,174,199,189,153,164,175,200,190,154,162,176,198,191,155,163,663,664,662,661,309,121,626,619,115,310,624,620,122,116,311,120,625,618,114,124,308,629,622,118,125,306,627,623,119,123,307,628,621,117,632,127,617,300,113,630,128,615,301,111,631,126,616,302,112,130,635,613,303,109,131,633,614,304,110,129,634,612,305,108,682,683,684,681,532,648,650,649,651,533,654,653,652,655,531,657,658,656,659,645,528,646,644,647,636,529,638,637,639,640,530,642,641,643,73,60,70,538,80,74,61,71,539,78,72,62,69,537,79,63,76,66,534,83,64,77,67,535,81,65,75,68,536,82,695,696,693,694,217,471,496,483,506,218,497,484,472,504,216,473,495,485,505,470,220,492,482,509,468,221,493,480,507,469,219,494,481,508,502,477,489,223,512,503,478,490,224,510,501,479,491,222,511,476,498,488,226,515,474,499,486,227,513,475,500,487,225,514,667,668,665,666,138,337,314,359,326,139,312,357,338,324,140,336,313,358,325,340,141,317,355,329,341,142,315,356,327,339,143,316,354,328,320,343,350,136,332,318,344,348,137,330,319,342,349,135,331,346,323,353,132,335,347,321,351,133,333,345,322,352,134,334,675,676,673,674 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#520f0c8ba72cb86fc7f95b2cd25444b775e13567ed9a2b839438811596de084e, 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 17:24:10 · history