Equation 677 Database

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Magma 259e97ae9455…

magma 259e97ae9455
Size
705
Isomorphism class hash
259e97ae9455353be680c7d131b01add01e3e2f57e85735c15184bf5b2a6569a
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 21:48:59
Display reorder
660,502,501,503,500,498,499,492,493,494,495,496,497,478,479,477,474,475,476,469,470,468,472,473,471,297,298,299,296,294,295,288,289,290,291,292,293,412,413,411,408,409,410,418,419,417,414,415,416,64,65,63,60,61,62,70,71,69,66,67,68,686,700,693,697,481,480,482,483,484,485,486,487,488,489,490,491,442,443,441,438,439,440,433,434,432,436,437,435,462,463,464,465,466,467,460,461,459,456,457,458,453,454,455,452,450,451,444,445,446,447,448,449,430,431,429,426,427,428,421,422,420,424,425,423,687,701,694,695,39,41,40,37,38,36,47,45,46,43,44,42,595,596,594,598,599,597,593,591,592,589,590,588,568,569,567,564,565,566,574,575,573,570,571,572,602,600,601,605,603,604,608,606,607,611,609,610,584,582,583,587,585,586,579,580,581,578,576,577,662,674,669,667,94,93,95,92,90,91,84,85,86,87,88,89,618,619,620,621,622,623,616,617,615,612,613,614,641,639,640,637,638,636,647,645,646,643,644,642,632,630,631,635,633,634,627,628,629,626,624,625,657,658,659,656,654,655,648,649,650,651,652,653,661,670,684,683,307,306,308,309,310,311,304,305,303,300,301,302,373,374,372,376,377,375,379,380,378,382,383,381,397,398,396,400,401,399,403,404,402,406,407,405,395,393,394,391,392,390,386,384,385,389,387,388,362,360,361,365,363,364,368,366,367,371,369,370,688,704,692,698,11,10,9,6,7,8,0,2,1,4,5,3,319,320,318,322,323,321,317,315,316,313,314,312,340,341,339,336,337,338,346,347,345,342,343,344,326,324,325,329,327,328,332,330,331,335,333,334,356,354,355,359,357,358,351,352,353,350,348,349,685,703,690,699,83,82,81,78,79,80,73,74,72,76,77,75,259,260,258,262,263,261,257,255,256,253,254,252,281,279,280,277,278,276,287,285,286,283,284,282,266,264,265,269,267,268,272,270,271,275,273,274,245,243,244,241,242,240,251,249,250,247,248,246,689,702,691,696,35,34,33,30,31,32,25,26,24,28,29,27,221,219,220,217,218,216,227,225,226,223,224,222,195,196,197,194,192,193,201,202,203,200,198,199,239,237,238,235,236,234,230,228,229,233,231,232,204,205,206,207,208,209,210,211,212,213,214,215,663,675,678,679,191,190,189,186,187,188,181,182,180,184,185,183,106,107,105,102,103,104,97,98,96,100,101,99,128,126,127,131,129,130,123,124,125,122,120,121,118,119,117,114,115,116,109,110,108,112,113,111,136,137,135,132,133,134,142,143,141,138,139,140,665,671,681,682,49,48,50,51,52,53,54,55,56,57,58,59,154,155,153,150,151,152,145,146,144,148,149,147,176,174,175,179,177,178,171,172,173,170,168,169,166,167,165,162,163,164,157,158,156,160,161,159,20,18,19,23,21,22,15,16,17,14,12,13,666,673,668,680,505,504,506,507,508,509,510,511,512,513,514,515,517,518,516,520,521,519,523,524,522,526,527,525,548,546,547,551,549,550,543,544,545,542,540,541,537,538,539,536,534,535,528,529,530,531,532,533,556,557,555,552,553,554,562,563,561,558,559,560,664,672,676,677 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 = {62} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:49:00 · history