Equation 677 Database

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Magma 18fcba727ecf…

magma 18fcba727ecf
Size
705
Isomorphism class hash
18fcba727ecf107e2f6da4df9b69e2843d37132d61f2bb27aafb99a5e886dff9
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 21:48:49
Display reorder
660,288,290,289,293,291,292,296,294,295,299,297,298,69,70,71,68,66,67,60,61,62,63,64,65,222,223,224,225,226,227,220,221,219,216,217,218,570,571,572,573,574,575,568,569,567,564,565,566,428,426,427,431,429,430,423,424,425,422,420,421,676,692,690,683,600,602,601,605,603,604,608,606,607,611,609,610,474,475,476,477,478,479,472,473,471,468,469,470,191,189,190,187,188,186,182,180,181,185,183,184,488,486,487,491,489,490,483,484,485,482,480,481,325,326,324,328,329,327,331,332,330,334,335,333,687,693,701,697,413,412,411,408,409,410,418,419,417,414,415,416,279,280,281,278,276,277,285,286,287,284,282,283,553,554,552,556,557,555,559,560,558,562,563,561,209,207,208,205,206,204,215,213,214,211,212,210,271,272,270,274,275,273,269,267,268,265,266,264,666,670,678,672,193,192,194,195,196,197,198,199,200,201,202,203,338,336,337,341,339,340,344,342,343,347,345,346,135,136,137,134,132,133,141,142,143,140,138,139,500,498,499,503,501,502,495,496,497,494,492,493,612,613,614,615,616,617,618,619,620,621,622,623,674,681,689,684,29,28,27,24,25,26,34,35,33,30,31,32,635,633,634,631,632,630,626,624,625,629,627,628,145,146,144,148,149,147,151,152,150,154,155,153,355,356,354,358,359,357,353,351,352,349,350,348,505,506,504,508,509,507,511,512,510,514,515,513,688,700,704,698,651,653,652,649,650,648,659,657,658,655,656,654,381,382,383,380,378,379,372,373,374,375,376,377,245,243,244,241,242,240,251,249,250,247,248,246,236,234,235,239,237,238,231,232,233,230,228,229,536,534,535,539,537,538,531,532,533,530,528,529,685,695,703,699,74,73,72,76,77,75,79,80,78,82,83,81,89,87,88,85,86,84,95,93,94,91,92,90,102,103,104,105,106,107,100,101,99,96,97,98,116,114,115,119,117,118,111,112,113,110,108,109,121,122,120,124,125,123,127,128,126,130,131,129,661,662,667,663,157,156,158,159,160,161,162,163,164,165,166,167,309,310,311,308,306,307,300,301,302,303,304,305,443,441,442,439,440,438,434,432,433,437,435,436,578,576,577,581,579,580,584,582,583,587,585,586,454,455,453,450,451,452,445,446,444,448,449,447,675,680,691,682,549,551,550,547,548,546,542,540,541,545,543,544,252,253,254,255,256,257,258,259,260,261,262,263,396,397,398,399,400,401,402,403,404,405,406,407,395,393,394,391,392,390,386,384,385,389,387,388,23,21,22,19,20,18,14,12,13,17,15,16,686,694,702,696,38,37,36,40,41,39,43,44,42,46,47,45,4,5,3,1,0,2,10,11,9,6,7,8,362,360,361,365,363,364,368,366,367,371,369,370,524,522,523,527,525,526,519,520,521,518,516,517,637,638,636,640,641,639,643,644,642,646,647,645,665,669,679,671,169,168,170,171,172,173,174,175,176,177,178,179,57,58,59,56,54,55,48,49,50,51,52,53,463,464,462,466,467,465,461,459,460,457,458,456,323,321,322,319,320,318,314,312,313,317,315,316,591,592,593,590,588,589,597,598,599,596,594,595,664,668,677,673 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {62} 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 21:48:50 · history