Equation 677 Database

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Magma be75d4a9249f…

magma be75d4a9249f
Size
705
Isomorphism class hash
be75d4a9249fa27e60bbc465f8dbf1ca49dac370510b0ec06ba81868eadf2c20
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 21:23:47
Display reorder
660,605,628,427,593,617,606,629,425,594,618,604,630,426,592,616,631,430,596,620,608,632,609,428,597,621,633,607,429,595,619,599,433,611,634,623,431,612,635,600,624,432,610,636,598,622,614,436,637,602,626,615,434,638,603,627,613,435,639,601,625,687,688,686,685,93,286,205,296,481,94,284,203,297,479,95,285,204,298,480,282,208,295,484,96,283,97,206,293,482,281,98,207,294,483,302,200,91,292,476,201,92,290,303,477,202,90,291,304,478,87,199,288,301,475,88,197,289,299,473,89,198,287,300,474,703,704,701,702,47,106,583,420,14,45,107,584,421,12,46,105,585,419,13,109,582,423,10,50,110,48,580,424,11,108,49,581,422,9,418,589,42,104,5,590,43,102,416,3,591,44,103,417,4,41,588,100,414,8,39,586,101,415,6,40,587,99,413,7,671,672,670,669,310,70,216,493,23,308,71,217,491,21,309,69,215,492,22,73,219,496,26,306,74,307,220,494,24,72,305,218,495,25,488,214,316,68,18,212,314,66,489,19,213,315,67,490,20,312,210,64,487,17,313,211,65,485,15,311,209,63,486,16,679,680,678,677,520,35,83,505,317,518,33,81,503,318,519,34,82,504,319,38,86,508,320,516,36,517,84,506,321,37,515,85,507,322,500,78,511,30,323,79,509,31,501,324,80,510,32,502,325,514,77,29,499,326,512,75,27,497,327,513,76,28,498,328,692,691,690,689,367,392,553,354,387,365,393,551,355,388,366,394,552,353,386,391,556,357,383,370,389,368,554,358,384,390,369,555,356,385,360,548,373,398,378,549,371,399,361,379,550,372,400,359,377,376,547,397,363,381,374,545,395,364,382,375,546,396,362,380,699,700,698,697,145,160,113,132,151,146,161,111,133,152,144,159,112,134,150,163,116,131,147,141,164,142,114,129,148,162,143,115,130,149,123,119,136,166,157,117,137,167,124,158,118,135,165,125,156,139,122,169,126,153,140,120,170,127,154,138,121,168,128,155,663,664,662,661,234,453,642,222,444,235,454,640,223,445,233,452,641,221,443,449,645,225,447,237,450,238,643,226,448,451,236,644,224,446,228,648,240,459,442,646,241,460,229,440,647,239,458,227,441,243,651,455,231,438,244,649,456,232,439,242,650,457,230,437,682,683,684,681,570,564,408,569,2,571,565,409,567,1,572,563,407,568,0,566,411,171,178,573,652,654,412,653,655,658,659,410,656,657,174,406,574,562,181,404,575,560,172,179,405,576,561,173,180,577,402,558,177,184,578,403,559,175,182,579,401,557,176,183,695,696,693,694,528,340,52,341,536,529,338,53,342,537,527,339,51,343,538,336,55,344,535,531,337,532,56,345,533,335,530,54,346,534,347,58,526,331,542,59,524,329,348,543,57,525,330,349,544,522,61,334,350,541,523,62,332,351,539,521,60,333,352,540,667,668,665,666,253,274,464,196,267,251,272,465,194,268,252,273,466,195,266,270,463,192,263,256,271,254,461,193,264,269,255,462,191,265,187,470,248,280,258,471,249,278,185,259,472,250,279,186,257,247,469,276,190,261,245,467,277,188,262,246,468,275,189,260,675,676,673,674 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#ef4a4f27352a122a7b1088a6208971ffd57fb3858716fe27bd37fbc92d64744c, 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 21:23:47 · history