Equation 677 Database

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Magma 83fdf1fa9621…

magma 83fdf1fa9621
Size
705
Isomorphism class hash
83fdf1fa9621ccaa79464da6ced4178c86d87292f60736bc6fc40dfcf6e2f80c
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 19:43:38
Display reorder
660,612,589,267,601,577,613,590,268,602,578,614,588,269,600,576,592,615,266,604,580,593,616,264,605,581,617,591,265,603,579,273,595,618,607,583,274,596,619,608,584,275,594,620,606,582,598,272,621,610,586,599,270,622,611,587,597,271,623,609,585,687,688,686,685,387,370,49,383,350,388,371,50,381,348,389,369,48,382,349,366,386,52,379,353,367,384,53,380,351,385,368,51,378,352,55,361,393,374,356,56,362,394,372,354,54,360,395,373,355,364,58,392,377,359,365,59,390,375,357,363,57,391,376,358,703,704,701,702,113,78,252,100,572,111,79,253,101,570,112,80,254,99,571,81,109,255,96,575,82,110,256,97,573,108,83,257,98,574,258,84,104,91,567,259,85,102,92,568,260,86,103,90,569,87,261,107,94,566,88,262,105,95,564,89,263,106,93,565,671,672,670,669,437,418,180,431,398,435,419,181,429,396,436,417,182,430,397,414,433,183,427,401,415,434,184,428,399,432,416,185,426,400,178,409,443,422,404,179,410,441,420,402,177,408,442,421,403,412,174,439,425,407,413,175,440,423,405,411,176,438,424,406,679,680,678,677,480,457,187,469,445,481,458,188,470,446,482,456,186,468,444,460,483,190,472,448,461,484,191,473,449,485,459,189,471,447,193,463,486,475,451,194,464,487,476,452,192,462,488,474,450,466,196,489,478,454,467,197,490,479,455,465,195,491,477,453,692,691,690,689,531,507,237,519,544,532,508,238,520,545,533,509,239,521,543,506,530,236,518,540,504,528,234,516,541,529,505,235,517,542,243,513,537,525,550,244,514,538,526,551,245,515,539,527,549,512,242,536,524,546,510,240,534,522,547,511,241,535,523,548,699,700,698,697,122,148,28,43,126,120,149,29,44,127,121,147,27,42,128,144,125,24,46,129,145,123,25,47,130,124,146,26,45,131,34,139,117,41,132,35,140,118,39,133,33,138,119,40,134,142,30,116,37,135,143,31,114,38,136,141,32,115,36,137,663,664,662,661,293,68,626,283,151,291,66,624,284,152,292,67,625,282,150,71,289,629,286,154,69,290,627,287,155,288,70,628,285,153,632,63,299,281,157,630,64,297,279,158,631,65,298,280,156,62,635,295,277,160,60,633,296,278,161,61,634,294,276,159,682,683,684,681,651,649,169,648,650,655,652,170,653,654,659,656,168,657,658,645,647,172,646,644,636,638,173,637,639,643,641,171,642,640,167,249,559,77,557,165,250,560,75,555,166,251,558,76,556,248,163,562,73,553,246,164,563,74,554,247,162,561,72,552,695,696,693,694,232,206,503,212,6,233,204,501,210,7,231,205,502,211,8,209,228,499,215,9,207,229,500,213,10,230,208,498,214,11,494,201,223,218,4,492,202,224,216,5,493,203,222,217,3,200,497,226,221,1,198,495,227,219,0,199,496,225,220,2,667,668,665,666,337,323,19,329,310,338,321,20,327,311,336,322,18,328,309,319,340,22,325,306,320,341,23,326,307,339,318,21,324,308,17,314,343,335,301,15,312,344,333,302,16,313,342,334,300,317,13,346,331,304,315,14,347,332,305,316,12,345,330,303,675,676,673,674 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#a687d51fdba056b88b615f4c33c4bd51079879725771af3a621b4a64ac93acf2, 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 19:43:39 · history