Equation 677 Database

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Magma 361368219f73…

magma 361368219f73
Size
705
Isomorphism class hash
361368219f7366873bfb05748093ca1faf15460823bee0c85be77cea69ccaa25
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 15:33:42
Display reorder
660,17,16,15,12,13,14,22,23,21,18,19,20,498,499,500,501,502,503,496,497,495,492,493,494,510,511,512,513,514,515,508,509,507,504,505,506,89,87,88,85,86,84,95,93,94,91,92,90,30,31,32,33,34,35,28,29,27,24,25,26,688,684,679,687,650,649,648,652,653,651,655,656,654,658,659,657,613,614,612,616,617,615,619,620,618,622,623,621,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,255,256,257,254,252,253,261,262,263,260,258,259,697,689,693,701,240,242,241,245,243,244,248,246,247,251,249,250,215,213,214,211,212,210,206,204,205,209,207,208,226,227,225,222,223,224,217,218,216,220,221,219,239,237,238,235,236,234,230,228,229,233,231,232,490,491,489,486,487,488,481,482,480,484,485,483,665,673,667,676,64,63,65,62,60,61,69,70,71,68,66,67,272,270,271,275,273,274,267,268,269,266,264,265,284,282,283,287,285,286,279,280,281,278,276,277,296,294,295,299,297,298,291,292,293,290,288,289,1,0,2,3,4,5,6,7,8,9,10,11,681,677,678,685,333,335,334,331,332,330,326,324,325,329,327,328,345,346,347,344,342,343,336,337,338,339,340,341,300,301,302,303,304,305,306,307,308,309,310,311,314,312,313,317,315,316,320,318,319,323,321,322,38,36,37,41,39,40,44,42,43,47,45,46,696,695,694,702,403,402,404,405,406,407,400,401,399,396,397,398,409,410,408,412,413,411,415,416,414,418,419,417,421,422,420,424,425,423,427,428,426,430,431,429,392,390,391,395,393,394,387,388,389,386,384,385,191,189,190,187,188,186,182,180,181,185,183,184,690,700,692,704,154,153,155,152,150,151,144,145,146,147,148,149,159,160,161,158,156,157,165,166,167,164,162,163,171,172,173,170,168,169,177,178,179,176,174,175,139,140,138,142,143,141,137,135,136,133,134,132,131,129,130,127,128,126,122,120,121,125,123,124,661,662,663,664,535,534,536,537,538,539,532,533,531,528,529,530,541,542,540,544,545,543,547,548,546,550,551,549,552,553,554,555,556,557,558,559,560,561,562,563,524,522,523,527,525,526,519,520,521,518,516,517,112,113,111,108,109,110,118,119,117,114,115,116,682,683,680,686,445,444,446,447,448,449,450,451,452,453,454,455,457,458,456,460,461,459,463,464,462,466,467,465,469,470,468,472,473,471,475,476,474,478,479,477,433,434,432,436,437,435,439,440,438,442,443,441,195,196,197,194,192,193,201,202,203,200,198,199,691,699,698,703,52,51,53,50,48,49,57,58,59,56,54,55,355,356,354,358,359,357,353,351,352,349,350,348,367,368,366,370,371,369,365,363,364,361,362,360,379,380,378,382,383,381,377,375,376,373,374,372,74,72,73,77,75,76,80,78,79,83,81,82,670,671,668,674,577,576,578,579,580,581,582,583,584,585,586,587,589,590,588,592,593,591,595,596,594,598,599,597,601,602,600,604,605,603,607,608,606,610,611,609,565,566,564,568,569,567,571,572,570,574,575,573,105,106,107,104,102,103,96,97,98,99,100,101,669,672,666,675 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, 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 15:33:43 · history