Equation 677 Database

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Magma 4dcff00e08c5…

magma 4dcff00e08c5
Size
705
Isomorphism class hash
4dcff00e08c5999827add4f59e6ef8136ab64c6498b920638fdb141aa53ced08
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 16:52:24
Display reorder
660,142,545,579,557,569,143,555,543,580,567,141,556,544,581,568,138,541,553,578,565,139,542,554,576,566,140,540,552,577,564,585,551,133,563,575,586,549,134,561,573,587,550,132,562,574,547,584,136,559,571,548,582,137,560,572,546,583,135,558,570,687,688,686,685,84,377,358,388,347,85,389,375,359,345,86,387,376,357,346,87,373,384,354,343,88,374,385,355,344,89,372,386,356,342,364,368,82,379,353,365,366,83,380,351,363,367,81,378,352,371,360,78,382,349,369,361,79,383,350,370,362,80,381,348,703,704,701,702,103,538,522,113,124,104,111,539,523,125,102,112,537,524,123,106,534,109,525,120,107,535,110,526,121,105,536,108,527,122,520,529,101,119,130,521,530,99,117,131,519,528,100,118,129,532,516,97,115,126,533,517,98,116,127,531,518,96,114,128,671,672,670,669,2,227,208,145,396,1,146,225,209,397,0,144,226,207,398,5,223,148,204,399,3,224,149,205,400,4,222,147,206,401,214,218,8,151,394,215,216,6,152,395,213,217,7,150,393,221,210,11,154,390,219,211,9,155,391,220,212,10,153,392,679,680,678,677,239,447,430,403,414,237,404,448,431,415,238,402,449,429,416,235,446,406,426,417,236,444,407,427,418,234,445,405,428,419,436,438,230,409,420,437,439,228,410,421,435,440,229,408,422,441,432,233,412,423,442,433,231,413,424,443,434,232,411,425,692,691,690,689,178,244,279,180,504,179,181,245,280,505,177,182,243,281,506,174,240,183,278,507,175,241,184,276,508,176,242,185,277,509,285,250,169,186,502,286,251,170,187,503,287,249,168,188,501,246,284,172,189,498,247,282,173,190,499,248,283,171,191,500,699,700,698,697,13,44,38,60,77,14,61,42,36,75,12,62,43,37,76,16,47,63,41,73,17,45,64,39,74,15,46,65,40,72,33,50,19,58,68,34,48,20,59,66,35,49,18,57,67,53,32,22,54,71,51,30,23,55,69,52,31,21,56,70,663,664,662,661,253,599,626,611,622,254,609,597,624,623,252,610,598,625,621,256,595,607,629,618,257,596,608,627,619,255,594,606,628,620,632,590,259,602,613,630,588,260,600,614,631,589,258,601,612,593,635,262,605,616,591,633,263,603,617,592,634,261,604,615,682,683,684,681,203,649,650,651,648,201,655,652,654,653,202,659,656,658,657,199,646,647,644,645,200,636,638,637,639,198,640,643,642,641,91,291,194,513,25,92,292,192,514,26,90,293,193,515,24,290,94,197,512,28,288,95,195,510,29,289,93,196,511,27,695,696,693,694,156,454,490,472,474,157,473,455,491,475,158,471,453,489,476,159,450,468,486,477,160,451,469,487,478,161,452,470,488,479,496,460,162,463,480,497,461,163,464,481,495,459,164,462,482,456,492,165,466,483,457,493,166,467,484,458,494,167,465,485,667,668,665,666,264,317,305,329,340,265,327,315,303,341,266,328,316,304,339,267,313,325,301,336,268,314,326,302,337,269,312,324,300,338,296,308,270,320,331,294,306,271,318,332,295,307,272,319,330,311,299,273,323,334,309,297,274,321,335,310,298,275,322,333,675,676,673,674 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#458b3cfe489c9903ffdf95802569f7fced83cfa9f913419e94bc2fd3ec4c05bf, 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 16:52:25 · history