Equation 677 Database

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Magma 5ae16b9e4fd3…

magma 5ae16b9e4fd3
Size
705
Isomorphism class hash
5ae16b9e4fd339b599462bc01e4d2c1754fb56035864a09a94fb31635dbd2049
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 21:22:59
Display reorder
660,349,87,316,352,333,350,88,317,353,331,351,89,354,318,332,348,86,319,355,329,346,84,320,356,330,347,85,321,357,328,93,340,322,358,339,94,341,323,359,337,95,342,324,360,338,343,92,325,361,335,344,90,326,362,336,345,91,327,363,334,685,686,688,687,206,123,408,77,201,204,124,406,75,202,205,125,76,407,203,209,122,411,73,200,207,120,409,74,198,208,121,410,72,199,129,212,403,83,192,130,210,404,81,193,131,211,405,82,194,215,128,402,79,195,213,126,400,80,196,214,127,401,78,197,701,702,704,703,544,307,577,559,541,545,308,578,560,542,546,309,561,579,543,547,306,576,558,540,548,304,574,556,538,549,305,575,557,539,313,550,568,565,532,314,551,569,566,533,315,552,570,567,534,553,312,571,564,535,554,310,572,562,536,555,311,573,563,537,670,669,672,671,441,133,420,224,424,439,134,418,222,425,440,132,223,419,426,437,136,423,227,427,438,137,421,225,428,436,135,422,226,429,139,447,415,219,430,140,445,416,220,431,138,446,417,221,432,443,142,414,218,433,444,143,412,216,434,442,141,413,217,435,680,677,679,678,29,449,234,150,240,27,450,235,151,241,28,448,152,236,242,25,452,237,153,243,26,453,238,154,244,24,451,239,155,245,455,35,232,148,246,456,33,233,149,247,454,34,231,147,248,31,458,228,144,249,32,459,229,145,250,30,457,230,146,251,689,690,691,692,509,264,489,476,505,510,265,487,477,506,508,266,475,488,507,512,267,485,472,504,513,268,486,473,502,511,269,484,474,503,270,515,495,482,496,271,516,493,483,497,272,514,494,481,498,518,273,491,478,499,519,274,492,479,500,517,275,490,480,501,697,698,700,699,608,591,639,619,602,609,589,637,620,603,607,590,621,638,601,604,587,635,618,598,605,588,636,616,599,606,586,634,617,600,582,614,630,625,593,580,615,628,626,594,581,613,629,627,592,610,585,633,624,596,611,583,631,622,597,612,584,632,623,595,661,662,664,663,107,366,162,10,170,105,364,163,11,168,106,365,9,164,169,103,369,165,6,173,104,367,166,7,171,102,368,167,8,172,372,98,160,0,176,370,96,161,2,174,371,97,159,1,175,101,375,156,4,179,99,373,157,5,177,100,374,158,3,178,682,681,684,683,287,520,298,293,281,288,521,299,291,282,289,522,292,297,280,286,523,301,296,277,284,524,302,294,278,285,525,300,295,279,526,646,647,644,645,527,290,303,283,276,528,640,642,641,643,658,529,659,657,656,650,530,651,648,649,654,531,655,652,653,693,694,696,695,22,252,46,468,53,23,253,47,466,51,21,254,467,45,52,18,255,42,471,49,19,256,43,469,50,20,257,44,470,48,258,13,37,463,59,259,14,38,464,57,260,12,36,465,58,16,261,40,462,55,17,262,41,460,56,15,263,39,461,54,666,665,668,667,389,60,187,116,382,390,61,188,114,383,388,62,115,186,384,392,63,190,119,385,393,64,191,117,386,391,65,189,118,387,66,395,185,111,380,67,396,183,112,381,68,394,184,113,379,398,69,181,110,376,399,70,182,108,377,397,71,180,109,378,674,673,676,675 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#edd749230bc58665165cb5ff86cf593765d0cefcd490b689f1cd7ce77c95b856, 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 21:23:00 · history