Equation 677 Database

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Magma 7a4a38245b15…

magma 7a4a38245b15
Size
705
Isomorphism class hash
7a4a38245b1589d89160e12aae1a173dc76af59d8e88055870d23b6287b6859e
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 19:42:01
Display reorder
660,363,350,53,133,369,364,51,134,370,348,365,349,52,132,371,353,362,49,136,368,351,360,50,137,366,352,361,48,135,367,59,354,345,139,375,57,355,346,140,376,58,356,347,138,377,357,55,344,142,374,358,56,342,143,372,359,54,343,141,373,685,686,688,687,496,482,240,183,177,497,241,184,178,480,495,481,242,185,179,485,492,243,182,176,483,493,244,180,174,484,494,245,181,175,246,487,477,189,168,247,488,478,190,169,248,486,479,191,170,490,249,476,188,171,491,250,474,186,172,489,251,475,187,173,701,702,704,703,340,616,127,614,599,341,128,615,600,617,339,618,126,613,598,619,336,130,610,602,620,337,131,611,603,621,338,129,612,601,125,331,622,605,597,123,332,623,606,595,124,330,624,604,596,334,121,625,608,593,335,122,626,609,594,333,120,627,607,592,670,669,672,671,209,203,504,260,66,207,505,258,67,201,208,202,506,259,68,199,205,507,263,69,200,206,508,261,70,198,204,509,262,71,502,215,194,255,64,503,213,192,256,65,501,214,193,257,63,211,498,197,254,60,212,499,195,252,61,210,500,196,253,62,680,677,679,678,220,272,512,72,237,221,510,73,238,270,219,271,511,74,239,275,216,515,75,236,273,217,513,76,234,274,218,514,77,235,518,226,267,78,228,516,227,268,79,229,517,225,269,80,230,222,521,266,81,231,223,519,264,82,232,224,520,265,83,233,689,690,691,692,100,90,293,6,578,101,291,7,576,91,99,92,292,8,577,93,96,289,9,581,94,97,290,10,579,95,98,288,11,580,299,106,88,4,573,297,107,89,5,574,298,105,87,3,575,102,295,84,1,572,103,296,85,0,570,104,294,86,2,571,697,698,700,699,635,31,651,15,45,636,649,16,46,32,634,30,650,17,47,34,638,647,14,44,35,639,648,12,42,33,637,646,13,43,642,633,29,21,36,640,631,27,22,37,641,632,28,23,38,629,645,25,20,39,630,643,26,18,40,628,644,24,19,41,661,662,664,663,394,384,155,414,412,395,153,415,413,385,393,386,154,416,411,387,390,151,417,408,388,391,152,418,409,389,392,150,419,410,146,400,382,420,403,144,401,383,421,404,145,399,381,422,402,396,149,378,423,406,397,147,379,424,407,398,148,380,425,405,682,681,684,683,314,308,116,588,318,315,114,586,316,306,313,307,115,587,317,304,310,119,591,321,305,311,117,589,319,303,312,118,590,320,111,658,657,659,656,112,309,326,585,322,113,653,652,654,655,329,110,302,584,325,327,108,300,582,323,328,109,301,583,324,693,694,696,695,524,560,280,548,536,522,281,546,534,558,523,559,279,547,535,563,527,276,551,539,561,525,277,549,537,562,526,278,550,538,286,530,566,554,542,287,528,564,552,540,285,529,565,553,541,533,282,569,557,545,531,283,567,555,543,532,284,568,556,544,666,665,668,667,463,451,163,439,427,464,164,440,428,452,462,450,162,438,426,454,466,166,442,430,455,467,167,443,431,453,465,165,441,429,161,469,457,445,433,159,470,458,446,434,160,468,456,444,432,472,157,460,448,436,473,158,461,449,437,471,156,459,447,435,674,673,676,675 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#a3dbb2a8d5932ce23601e140d077e70c3bff24b108fb14183b80120946e543a6, 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 19:42:02 · history