Equation 677 Database

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Magma fd49d1343212…

magma fd49d1343212
Size
705
Isomorphism class hash
fd49d1343212e8f833881f247d672567cfdc64be574993a878b01e25afd45f85
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 21:44:57
Display reorder
660,164,182,332,173,340,162,180,171,330,341,181,172,163,331,339,167,185,169,335,336,165,183,170,333,337,166,184,168,334,338,188,327,159,179,346,186,328,160,177,347,187,329,161,178,345,191,326,158,175,342,324,189,156,176,343,190,325,157,174,344,685,686,688,687,405,145,115,137,130,406,146,135,116,131,144,136,407,114,129,404,148,133,118,126,402,149,134,119,127,403,147,132,117,128,151,113,396,143,121,152,111,397,141,122,150,112,398,142,120,154,109,399,139,124,110,155,400,140,125,153,108,401,138,123,701,702,704,703,322,575,587,611,599,323,573,609,585,597,574,610,321,586,598,318,571,607,583,595,319,572,608,584,596,320,570,606,582,594,566,578,313,602,590,564,576,314,600,588,565,577,312,601,589,569,581,316,605,593,579,567,317,603,591,568,580,315,604,592,670,669,672,671,106,414,431,449,442,107,415,447,429,443,416,448,105,430,441,102,417,445,427,438,103,418,446,428,439,104,419,444,426,440,412,422,97,455,433,413,420,98,453,434,411,421,96,454,432,408,425,100,451,436,423,409,101,452,437,410,424,99,450,435,680,677,679,678,223,485,494,477,467,224,483,478,492,465,484,479,222,493,466,226,481,476,497,463,227,482,474,495,464,225,480,475,496,462,491,500,221,468,458,489,498,219,469,456,490,499,220,470,457,487,503,217,471,461,501,488,218,472,459,486,502,216,473,460,689,690,691,692,86,545,276,538,523,84,543,539,277,524,544,537,85,278,522,82,541,534,279,526,83,542,535,280,527,81,540,536,281,525,551,282,77,529,521,549,283,75,530,519,550,284,76,528,520,547,285,80,532,517,286,548,78,533,518,546,287,79,531,516,697,698,700,699,195,635,647,619,204,196,633,620,645,205,634,618,197,646,206,194,631,622,643,207,192,632,623,644,208,193,630,621,642,209,626,638,201,617,210,624,636,202,615,211,625,637,203,616,212,629,641,200,613,213,639,627,198,614,214,628,640,199,612,215,661,662,664,663,359,44,53,36,26,357,42,37,51,24,43,38,358,52,25,355,40,35,56,22,356,41,33,54,23,354,39,34,55,21,50,59,350,27,17,48,57,348,28,15,49,58,349,29,16,46,62,353,30,20,60,47,351,31,18,45,61,352,32,19,682,681,684,683,560,297,310,92,291,558,298,90,311,292,299,91,559,309,293,563,300,88,306,290,561,301,89,307,288,562,302,87,308,289,654,655,555,653,652,658,659,556,657,656,649,650,557,648,651,2,304,554,94,296,305,1,552,95,294,0,303,553,93,295,693,694,696,695,506,264,234,255,249,504,265,256,235,250,266,257,505,236,251,509,267,254,237,248,507,268,252,238,246,508,269,253,239,247,270,232,512,261,240,271,233,510,262,241,272,231,511,263,242,273,228,515,260,243,229,274,513,258,244,275,230,514,259,245,666,665,668,667,8,383,395,367,71,6,381,368,393,69,382,366,7,394,70,4,379,370,391,74,5,380,371,392,72,3,378,369,390,73,374,386,14,365,66,372,384,12,363,67,373,385,13,364,68,377,389,10,361,65,387,375,11,362,63,376,388,9,360,64,674,673,676,675 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#f1e2c600ebf06c2e31b8968226514217c5fc265d2577d787fe558118ce3f2b96, 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 21:44:58 · history