Equation 677 Database

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Magma edeac458fec1…

magma edeac458fec1
Size
705
Isomorphism class hash
edeac458fec13a19723cd67c96128bc163df54faffc08a040105dc1bd23765b6
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 20:35:19
Display reorder
660,281,613,621,131,604,282,602,611,622,132,612,603,283,620,133,280,609,607,624,130,610,278,605,625,128,279,608,606,623,129,287,619,599,627,122,288,617,600,628,123,626,289,618,601,124,615,286,598,630,125,616,284,596,631,126,614,285,597,629,127,687,688,686,685,376,163,171,192,203,374,204,161,172,193,162,205,375,170,191,379,159,202,174,188,160,377,200,175,189,378,158,201,173,190,382,169,194,177,183,380,167,195,178,184,176,381,168,196,182,165,385,197,180,186,166,383,198,181,187,164,384,199,179,185,703,704,701,702,276,553,561,582,595,277,593,551,562,583,552,594,275,560,581,272,549,591,564,578,550,273,592,565,579,274,548,590,563,580,267,559,586,567,573,268,557,584,568,574,566,266,558,585,572,555,270,589,570,576,556,271,587,571,577,554,269,588,569,575,671,672,670,669,4,216,227,232,394,2,392,217,228,230,215,393,3,229,231,7,212,397,226,235,213,5,395,224,233,6,214,396,225,234,10,207,389,218,238,8,208,390,219,236,220,9,206,391,237,210,13,388,221,241,211,11,386,222,239,209,12,387,223,240,679,680,678,677,116,59,406,413,242,117,243,60,404,414,61,244,118,405,415,119,58,245,409,412,56,120,246,407,410,121,57,247,408,411,114,50,248,401,419,115,51,249,402,420,403,113,52,250,421,53,110,251,400,418,54,111,252,398,416,55,112,253,399,417,692,691,690,689,326,517,472,491,496,327,494,515,470,492,516,495,328,471,493,329,513,499,475,490,514,330,497,473,488,331,512,498,474,489,332,508,502,478,482,333,506,500,476,483,477,334,507,501,484,511,335,505,481,485,509,336,503,479,486,510,337,504,480,487,699,700,698,697,23,69,27,47,104,24,105,70,28,48,68,106,25,26,49,22,72,107,30,46,73,20,108,31,44,21,71,109,29,45,14,67,102,33,38,15,65,103,34,39,32,16,66,101,40,63,17,98,36,41,64,18,99,37,42,62,19,100,35,43,663,664,662,661,634,138,344,297,307,632,305,139,345,298,137,306,633,346,296,637,134,303,347,300,135,635,304,348,301,636,136,302,349,299,640,144,313,342,295,638,145,311,343,293,341,639,143,312,294,140,643,309,338,291,141,641,310,339,292,142,642,308,340,290,682,683,684,681,76,657,658,659,656,74,648,649,650,651,653,652,75,654,655,79,0,525,533,546,645,77,644,646,647,78,1,524,532,547,82,531,520,536,541,80,529,518,534,542,535,81,530,519,540,527,85,523,539,544,528,83,521,537,545,526,84,522,538,543,695,696,693,694,265,436,455,458,431,263,432,434,456,459,435,433,264,457,460,261,439,430,454,461,437,262,428,452,462,260,438,429,453,463,256,442,422,446,464,254,440,423,447,465,448,255,441,424,466,445,259,425,449,467,443,257,426,450,468,444,258,427,451,469,667,668,665,666,91,324,146,358,367,89,365,325,147,356,323,366,90,148,357,87,320,363,149,361,321,88,364,150,359,86,322,362,151,360,97,315,373,152,353,95,316,371,153,354,154,96,314,372,355,318,93,369,155,352,319,94,370,156,350,317,92,368,157,351,675,676,673,674 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#c683f2f4b9bca41895c10e0d2ae80f929e5396dd75ded79bce8025bcd75f3dbe, 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 20:35:20 · history