Equation 677 Database

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Magma 5540cb12c8ac…

magma 5540cb12c8ac
Size
705
Isomorphism class hash
5540cb12c8ac8ae939292bf0fef7fcea29eb2ab942b6694a6930319397a760b5
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 19:55:48
Display reorder
660,573,71,584,549,561,574,72,585,550,562,572,73,586,548,560,70,576,587,552,564,68,577,588,553,565,69,575,589,551,563,579,62,590,555,567,580,63,591,556,568,578,64,592,554,566,65,582,593,558,570,66,583,594,559,571,67,581,595,557,569,687,688,686,685,337,152,349,360,325,338,153,350,361,326,336,154,348,362,324,155,340,352,363,328,156,341,353,364,329,157,339,351,365,327,343,150,355,366,331,344,151,356,367,332,342,149,354,368,330,146,346,358,369,334,147,347,359,370,335,148,345,357,371,333,703,704,701,702,539,97,505,516,524,540,95,503,517,525,541,96,504,515,526,93,538,501,512,527,94,536,502,513,528,92,537,500,514,529,545,88,511,522,530,546,86,509,523,531,547,87,510,521,532,91,544,507,518,533,89,542,508,519,534,90,543,506,520,535,671,672,670,669,380,173,389,401,411,378,174,387,399,412,379,172,388,400,413,176,383,385,397,410,177,381,386,398,408,175,382,384,396,409,375,179,395,407,417,376,180,393,405,418,377,178,394,406,419,182,374,391,403,416,183,372,392,404,414,181,373,390,402,415,679,680,678,677,207,426,58,21,191,205,427,56,22,192,206,428,57,20,190,429,203,61,24,194,430,204,59,25,195,431,202,60,23,193,198,424,53,19,189,196,425,54,17,187,197,423,55,18,188,420,201,52,15,185,421,199,50,16,186,422,200,51,14,184,692,691,690,689,252,229,268,80,486,253,230,269,81,487,254,231,267,82,488,228,255,264,83,489,226,256,265,84,490,227,257,266,85,491,258,220,274,78,484,259,221,275,79,485,260,222,273,77,483,223,261,270,74,480,224,262,271,75,481,225,263,272,76,482,699,700,698,697,123,8,44,106,113,124,9,45,104,114,122,10,46,105,115,11,126,47,109,112,12,127,48,107,110,13,125,49,108,111,129,6,42,101,119,130,7,43,102,120,128,5,41,103,121,2,132,38,100,118,3,133,39,98,116,4,131,40,99,117,663,664,662,661,634,277,596,611,621,632,278,597,612,622,633,276,598,613,620,280,637,599,610,624,281,635,600,608,625,279,636,601,609,623,640,283,602,617,627,638,284,603,618,628,639,282,604,619,626,286,643,605,616,630,287,641,606,614,631,285,642,607,615,629,682,683,684,681,656,26,657,659,658,648,27,649,651,650,652,28,653,655,654,29,165,1,498,233,30,644,645,646,647,31,164,0,499,232,160,32,171,496,237,158,33,169,497,238,159,34,170,495,239,35,163,167,492,236,36,161,168,493,234,37,162,166,494,235,695,696,693,694,472,214,436,445,456,473,215,437,446,457,471,216,435,444,458,217,468,432,448,459,218,469,433,449,460,219,470,434,447,461,478,212,442,451,462,479,213,443,452,463,477,211,441,450,464,208,474,438,454,465,209,475,439,455,466,210,476,440,453,467,667,668,665,666,312,135,250,296,304,313,136,251,294,305,314,134,249,295,303,138,315,246,299,300,139,316,247,297,301,137,317,248,298,302,318,141,241,291,310,319,142,242,292,311,320,140,240,293,309,144,321,244,290,306,145,322,245,288,307,143,323,243,289,308,675,676,673,674 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#b42b2593cdf495fd739236f86f5dbe699df6ba394eb7d6a8f934bf0cd7c90649, 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 19:55:48 · history