Equation 677 Database

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Magma 76c85b333555…

magma 76c85b333555
Size
705
Isomorphism class hash
76c85b3335550ffada1787d684c4dfa78a2cc2ea8b15de3683f0cc2707bab9d6
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 16:48:09
Display reorder
660,579,591,373,567,553,577,589,374,565,554,578,590,375,566,555,587,575,376,563,552,377,576,588,564,550,586,574,378,562,551,570,582,379,558,544,568,580,380,556,545,569,581,381,557,546,585,573,382,561,547,583,571,383,559,548,584,572,384,560,549,687,688,686,685,446,239,49,437,427,447,240,50,438,428,445,238,51,436,429,235,449,52,433,430,53,450,236,434,431,237,448,54,435,432,452,230,55,443,425,453,231,56,444,426,451,229,57,442,424,233,455,58,439,421,234,456,59,440,422,232,454,60,441,423,703,704,701,702,40,539,23,368,68,42,540,24,369,69,37,538,22,367,67,542,45,19,371,71,20,47,543,372,72,541,43,21,370,70,48,537,14,366,66,44,535,15,364,64,46,536,13,365,65,533,39,17,362,62,534,41,18,363,63,532,38,16,361,61,671,672,670,669,267,463,12,255,248,265,464,10,253,249,266,465,11,254,247,466,270,8,258,251,9,268,467,256,252,468,269,7,257,250,273,461,3,261,246,271,462,0,259,244,272,460,2,260,245,457,276,6,264,242,458,274,4,262,243,459,275,5,263,241,679,680,678,677,306,316,473,294,282,304,317,474,292,280,305,318,472,293,281,315,302,469,290,278,470,303,313,291,279,314,301,471,289,277,312,322,479,300,288,310,323,480,298,286,311,324,478,299,287,321,308,475,296,284,319,309,476,297,285,320,307,477,295,283,692,691,690,689,192,156,502,180,166,190,154,503,178,167,191,155,504,179,168,152,188,501,176,165,499,189,153,177,163,151,187,500,175,164,183,147,493,171,157,181,145,494,169,158,182,146,495,170,159,150,186,496,174,160,148,184,497,172,161,149,185,498,173,162,699,700,698,697,90,100,76,125,112,88,101,77,126,113,89,102,78,124,114,99,86,75,121,111,73,87,97,122,109,98,85,74,123,110,96,106,82,131,118,94,107,83,132,119,95,108,84,130,120,105,92,81,127,117,103,93,79,128,115,104,91,80,129,116,663,664,662,661,630,598,387,620,609,628,599,385,621,607,629,600,386,619,608,601,633,390,616,605,388,631,602,617,606,603,632,389,618,604,636,596,393,626,615,634,597,391,627,613,635,595,392,625,614,592,639,396,622,611,593,637,394,623,612,594,638,395,624,610,682,683,684,681,652,653,196,655,654,656,657,197,659,658,648,649,198,651,650,1,511,195,525,518,193,640,641,642,643,645,644,194,647,646,506,516,202,530,522,507,517,203,531,523,505,515,204,529,524,512,509,201,526,521,513,510,199,527,519,514,508,200,528,520,695,696,693,694,330,342,141,488,353,328,340,139,489,354,329,341,140,487,352,338,326,144,491,349,142,327,339,492,350,337,325,143,490,351,336,348,136,486,359,334,346,137,484,360,335,347,138,485,358,344,332,135,482,355,345,333,133,483,356,343,331,134,481,357,667,668,665,666,412,207,33,403,217,413,205,31,404,218,414,206,32,405,219,210,411,36,406,220,34,409,208,407,221,209,410,35,408,222,418,213,28,401,223,419,211,29,402,224,420,212,30,400,225,216,417,27,397,226,214,415,25,398,227,215,416,26,399,228,675,676,673,674 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#3f4c16e16e9bd422beeb4e3c1331ed0b07b0ac931af0d47b2d7497fadfe20a6b, 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 16:48:10 · history