Equation 677 Database

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Magma fd902df6a542…

magma fd902df6a542
Size
720
Isomorphism class hash
fd902df6a54217f08e794f524a3f65bbd38109326eba40eded58204088e1b147
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 11:14:28
Display reorder
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,719,174,152,145,175,153,146,176,154,147,177,155,148,178,156,149,179,157,135,165,158,136,166,159,137,167,160,138,168,161,139,169,162,140,170,163,141,171,164,142,172,150,143,144,173,151,183,190,191,192,193,194,180,181,182,185,186,187,188,189,184,698,696,695,697,10,344,322,11,330,323,12,331,324,13,332,325,14,333,326,1,334,327,0,335,328,2,336,329,3,337,315,4,338,316,5,339,317,6,340,318,7,341,319,8,342,320,321,9,343,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,718,715,717,716,130,109,103,131,110,104,132,111,90,133,112,91,134,113,92,120,114,93,121,115,94,122,116,95,123,117,96,124,118,97,125,119,98,126,105,99,127,106,100,128,107,101,102,129,108,85,77,78,79,80,81,82,83,84,87,88,89,75,76,86,683,685,684,686,384,364,358,385,365,359,386,366,345,387,367,346,388,368,347,389,369,348,375,370,349,376,371,350,377,372,351,378,373,352,379,374,353,380,360,354,381,361,355,382,362,356,357,383,363,393,400,401,402,403,404,390,391,392,395,396,397,398,399,394,693,691,694,692,456,435,430,457,436,431,458,437,432,459,438,433,460,439,434,461,440,420,462,441,421,463,442,422,464,443,423,450,444,424,451,445,425,452,446,426,453,447,427,454,448,428,429,455,449,412,419,405,406,407,408,409,410,411,414,415,416,417,418,413,705,703,706,704,549,528,577,550,529,578,551,530,579,552,531,580,553,532,581,554,533,582,540,534,583,541,535,584,542,536,570,543,537,571,544,538,572,545,539,573,546,525,574,547,526,575,576,548,527,559,566,567,568,569,555,556,557,558,561,562,563,564,565,560,709,708,710,707,654,62,56,655,63,57,656,64,58,657,65,59,658,66,45,659,67,46,645,68,47,646,69,48,647,70,49,648,71,50,649,72,51,650,73,52,651,74,53,652,60,54,55,653,61,38,30,31,32,33,34,35,36,37,40,41,42,43,44,39,677,678,676,675,196,244,238,197,245,239,198,246,225,199,247,226,200,248,227,201,249,228,202,250,229,203,251,230,204,252,231,205,253,232,206,254,233,207,240,234,208,241,235,209,242,236,237,195,243,219,211,212,213,214,215,216,217,218,221,222,223,224,210,220,699,702,700,701,588,636,629,589,637,615,590,638,616,591,639,617,592,640,618,593,641,619,594,642,620,595,643,621,596,644,622,597,630,623,598,631,624,599,632,625,585,633,626,586,634,627,628,587,635,612,604,605,606,607,608,609,610,611,614,600,601,602,603,613,712,714,711,713,498,493,473,499,494,474,500,480,475,501,481,476,502,482,477,503,483,478,504,484,479,505,485,465,506,486,466,507,487,467,508,488,468,509,489,469,495,490,470,496,491,471,472,497,492,523,515,516,517,518,519,520,521,522,510,511,512,513,514,524,680,682,679,681,282,261,309,283,262,310,284,263,311,270,264,312,271,265,313,272,266,314,273,267,300,274,268,301,275,269,302,276,255,303,277,256,304,278,257,305,279,258,306,280,259,307,308,281,260,290,297,298,299,285,286,287,288,289,292,293,294,295,296,291,687,688,690,689 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 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#9916b9303e5777c051d457f13e65b220048127e3f9475b765d37bfd24fd4df83, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 58, 75} 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 2026-10-06 11:14:30 · history