Equation 677 Database

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Magma 915261a152a6…

magma 915261a152a6
Size
705
Isomorphism class hash
915261a152a602cad3d93b930bfde95bd5528576d34612a943dd9f3eaa876ea5
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 21:49:35
Display reorder
660,60,62,61,65,63,64,68,66,67,71,69,70,93,94,95,92,90,91,84,85,86,87,88,89,79,80,78,82,83,81,77,75,76,73,74,72,372,373,374,375,376,377,378,379,380,381,382,383,57,58,59,56,54,55,48,49,50,51,52,53,672,692,682,683,430,429,431,428,426,427,420,421,422,423,424,425,448,449,447,444,445,446,454,455,453,450,451,452,434,432,433,437,435,436,440,438,439,443,441,442,29,25,27,35,30,32,41,36,39,47,42,45,413,411,412,409,410,408,419,417,418,415,416,414,688,704,696,698,345,347,346,343,344,342,338,336,337,341,339,340,364,365,363,360,361,362,370,371,369,366,367,368,350,348,349,353,351,352,356,354,355,359,357,358,19,20,18,22,23,21,17,15,16,13,14,12,325,326,324,328,329,327,331,332,330,334,335,333,666,674,669,679,475,474,476,477,478,479,472,473,471,468,469,470,493,494,492,496,497,495,499,500,498,502,503,501,484,485,483,480,481,482,490,491,489,486,487,488,274,275,273,270,271,272,265,266,264,268,269,267,463,464,462,466,467,465,461,459,460,457,458,456,671,690,685,684,515,514,513,510,511,512,505,506,504,508,509,507,291,292,293,290,288,289,297,298,299,296,294,295,276,277,278,279,280,281,282,283,284,285,286,287,196,197,195,192,193,194,202,203,201,198,199,200,310,311,309,306,307,308,301,302,300,304,305,303,689,703,695,700,609,611,610,607,608,606,602,600,601,605,603,604,585,586,587,584,582,583,576,577,578,579,580,581,571,572,570,574,575,573,569,567,568,565,566,564,2,1,0,5,3,4,8,6,7,11,9,10,593,591,592,589,590,588,599,597,598,595,596,594,686,702,694,697,226,225,227,224,222,223,216,217,218,219,220,221,243,244,245,242,240,241,249,250,251,248,246,247,230,228,229,233,231,232,236,234,235,239,237,238,210,211,212,213,214,215,208,209,207,204,205,206,263,261,262,259,260,258,254,252,253,257,255,256,661,663,662,667,103,102,104,105,106,107,100,101,99,96,97,98,121,122,120,124,125,123,127,128,126,130,131,129,112,113,111,108,109,110,118,119,117,114,115,116,384,385,386,387,388,389,390,391,392,393,394,395,134,132,133,137,135,136,140,138,139,143,141,142,673,691,681,687,653,652,651,648,649,650,658,659,657,654,655,656,627,628,629,626,624,625,633,634,635,632,630,631,613,614,612,616,617,615,619,620,618,622,623,621,318,319,320,321,322,323,316,317,315,312,313,314,646,647,645,642,643,644,637,638,636,640,641,639,680,701,699,693,540,542,541,545,543,544,548,546,547,551,549,550,519,520,521,518,516,517,525,526,527,524,522,523,559,560,558,562,563,561,557,555,556,553,554,552,34,31,33,26,28,24,46,43,44,38,40,37,537,538,539,536,534,535,528,529,530,531,532,533,664,675,670,678,144,146,145,149,147,148,152,150,151,155,153,154,177,178,179,176,174,175,168,169,170,171,172,173,163,164,162,166,167,165,161,159,160,157,158,156,403,404,402,406,407,405,401,399,400,397,398,396,184,185,183,180,181,182,190,191,189,186,187,188,665,676,668,677 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 = {63} 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 21:49:36 · history