Equation 677 Database

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Magma 520f271ac4ec…

magma 520f271ac4ec
Size
705
Isomorphism class hash
520f271ac4ecd8b21b071900fa8d8319a585e012b3fcdb4fbf1fe6395cc463e4
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 18:17:26
Display reorder
660,311,112,145,320,121,312,113,146,321,122,310,111,144,319,120,115,314,141,316,117,116,315,142,317,118,114,313,143,318,119,309,110,151,326,127,307,108,152,327,128,308,109,150,325,126,106,305,147,322,123,107,306,148,323,124,105,304,149,324,125,685,686,688,687,410,96,429,414,392,411,97,427,412,393,409,98,428,413,391,95,406,425,417,388,93,407,426,415,389,94,408,424,416,390,401,102,435,420,398,402,103,433,418,399,400,104,434,419,397,101,404,431,423,394,99,405,432,421,395,100,403,430,422,396,701,702,704,703,575,139,603,583,303,576,140,601,584,301,574,138,602,585,302,135,578,599,582,299,136,579,600,580,300,137,577,598,581,298,573,130,594,589,294,571,131,592,590,292,572,129,593,591,293,133,569,597,588,297,134,570,595,586,295,132,568,596,587,296,670,669,672,671,445,153,463,450,481,446,154,464,448,482,447,155,465,449,483,156,444,462,453,480,157,442,460,451,478,158,443,461,452,479,436,159,469,456,472,437,160,470,454,473,438,161,471,455,474,162,439,468,459,475,163,440,466,457,476,164,441,467,458,477,680,677,679,678,194,493,171,81,177,192,494,172,82,178,193,495,173,83,179,492,190,174,84,180,490,191,175,85,181,491,189,176,86,182,200,484,169,87,183,198,485,170,88,184,199,486,168,89,185,487,196,165,90,186,488,197,166,91,187,489,195,167,92,188,689,690,691,692,251,545,229,213,247,249,546,230,214,248,250,544,228,215,246,548,254,225,216,243,549,252,226,217,244,547,253,227,218,245,257,551,235,219,238,255,552,236,220,239,256,550,234,221,237,554,260,231,222,241,555,258,232,223,242,553,259,233,224,240,697,698,700,699,618,17,651,631,610,616,15,649,632,611,617,16,650,633,612,13,621,647,630,613,14,619,648,628,614,12,620,646,629,615,624,23,642,637,608,622,21,640,638,609,623,22,641,639,607,19,627,645,636,604,20,625,643,634,605,18,626,644,635,606,661,662,664,663,25,64,42,335,48,26,65,43,336,49,24,63,44,334,50,60,28,45,338,51,61,29,46,339,52,62,27,47,337,53,31,70,40,333,54,32,71,41,331,55,30,69,39,332,56,66,34,36,329,57,67,35,37,330,58,68,33,38,328,59,682,681,684,683,282,556,79,266,279,283,557,80,264,280,284,558,78,265,281,559,285,75,262,278,560,286,76,263,276,561,287,77,261,277,659,562,657,656,658,288,563,271,270,272,654,564,653,652,655,565,289,73,268,273,566,290,74,269,274,567,291,72,267,275,693,694,696,695,532,202,512,496,529,533,203,513,497,530,534,201,511,498,531,205,535,508,499,528,206,536,509,500,526,204,537,510,501,527,538,208,518,502,520,539,209,519,503,521,540,207,517,504,522,211,541,514,505,523,212,542,515,506,524,210,543,516,507,525,666,665,668,667,366,10,343,381,361,364,11,344,379,362,365,9,345,380,363,6,369,342,377,360,7,367,340,378,358,8,368,341,376,359,372,0,349,387,352,370,2,350,385,353,371,1,351,386,354,4,375,348,383,355,5,373,346,384,356,3,374,347,382,357,674,673,676,675 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#7662547f1ab019fdebb7f412cf128566d4c1d6f1fe751ad78d224fe85422d2cf, 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 18:17:27 · history