Equation 677 Database

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Magma 782a043abb93…

magma 782a043abb93
Size
705
Isomorphism class hash
782a043abb93b7a5ceba9ff5a4be0d7afef433aab56af96fef6a50c6315ae371
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 21:22:12
Display reorder
660,565,266,599,594,572,563,595,267,600,573,265,593,564,601,574,561,262,598,590,575,562,263,596,591,576,560,264,597,592,577,571,605,272,585,578,569,606,273,586,579,570,607,271,584,580,604,567,268,588,581,602,568,269,589,582,603,566,270,587,583,687,688,686,685,170,148,161,356,340,168,357,149,159,341,147,355,169,160,342,173,144,157,352,343,171,145,158,353,344,172,146,156,354,345,176,167,154,347,338,174,165,155,348,339,175,166,153,346,337,163,179,150,350,334,164,177,151,351,335,162,178,152,349,336,703,704,701,702,558,260,536,529,522,559,527,261,537,523,259,528,557,538,521,554,256,539,525,518,555,257,540,526,519,556,258,541,524,520,549,542,251,535,513,550,543,252,533,514,548,544,250,534,512,545,552,254,531,516,546,553,255,532,517,547,551,253,530,515,671,672,670,669,55,187,383,379,364,56,380,188,384,365,186,381,54,382,366,58,190,386,378,367,59,191,387,376,368,57,189,385,377,369,53,389,185,370,362,51,390,183,371,363,52,388,184,372,361,392,49,181,373,358,393,50,182,374,359,391,48,180,375,360,679,680,678,677,107,199,86,415,400,105,416,200,84,401,198,417,106,85,402,103,202,89,414,403,104,203,87,412,404,102,201,88,413,405,98,92,197,406,398,96,90,195,407,399,97,91,196,408,397,95,101,193,409,394,93,99,194,410,395,94,100,192,411,396,692,691,690,689,10,119,230,221,472,11,219,117,228,473,118,220,9,229,474,6,115,233,217,475,7,116,231,218,476,8,114,232,216,477,0,236,110,227,470,2,234,108,225,471,1,235,109,226,469,239,4,113,223,466,237,5,111,224,467,238,3,112,222,468,699,700,698,697,68,16,39,28,78,66,29,17,40,79,15,27,67,41,80,71,12,38,24,81,69,13,36,25,82,70,14,37,26,83,63,45,22,34,76,64,46,23,35,77,65,47,21,33,75,44,62,18,30,72,42,60,19,31,73,43,61,20,32,74,663,664,662,661,646,280,637,631,614,644,629,281,635,615,282,630,645,636,616,649,283,633,627,617,647,284,634,628,618,648,285,632,626,619,652,643,278,622,612,650,641,279,620,613,651,642,277,621,611,639,655,274,625,608,640,653,275,623,609,638,654,276,624,610,682,683,684,681,499,130,247,485,504,500,486,131,248,505,129,484,498,249,503,496,126,246,488,501,658,127,657,656,659,497,128,489,487,502,491,241,121,483,510,492,242,122,481,511,490,240,120,482,509,244,494,124,479,506,245,495,125,480,507,243,493,123,478,508,695,696,693,694,458,210,453,432,427,459,430,211,451,428,212,431,457,452,429,454,213,449,435,426,455,214,450,433,424,456,215,448,434,425,464,444,208,438,418,465,442,209,436,419,463,443,207,437,420,447,460,204,441,421,445,461,205,439,422,446,462,206,440,423,667,668,665,666,325,141,314,302,290,326,303,142,315,291,143,301,327,313,289,324,140,310,298,286,322,138,311,299,287,323,139,312,300,288,331,320,132,308,296,332,321,133,309,297,333,319,134,307,295,316,330,135,304,292,317,328,136,305,293,318,329,137,306,294,675,676,673,674 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#ebc786cbc6f59f4fde563d64e7e77b74986c3576b2c4677bed47ecf46da1acd3, 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 21:22:13 · history