Equation 677 Database

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Magma d754feab7612…

magma d754feab7612
Size
705
Isomorphism class hash
d754feab7612e2ec29fd4d3b6848565e7213c30c6e099cd5175786daf9e409d9
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 21:20:33
Display reorder
660,44,599,369,363,590,45,591,600,370,364,46,592,601,368,362,598,47,593,372,366,596,48,594,373,367,597,49,595,371,365,50,605,588,375,361,589,606,376,51,359,587,607,374,52,360,604,584,378,53,357,602,585,379,54,358,603,586,377,55,356,687,688,686,685,2,448,188,463,200,1,201,446,189,461,0,199,447,187,462,451,5,196,184,459,449,3,197,185,460,450,4,198,186,458,8,443,191,179,454,192,444,180,6,452,190,445,178,7,453,442,194,182,11,457,440,195,183,9,455,441,193,181,10,456,703,704,701,702,39,567,344,572,64,40,62,568,345,573,38,63,566,346,574,570,42,67,347,575,571,43,65,348,576,569,41,66,349,577,37,565,59,350,578,60,563,351,35,579,61,564,352,36,580,561,58,353,33,581,562,56,354,34,582,560,57,355,32,583,671,672,670,669,464,238,218,208,229,465,230,239,219,209,466,231,240,217,210,241,467,228,214,211,242,468,226,215,212,243,469,227,216,213,470,244,235,224,206,236,245,225,471,207,237,246,223,472,205,247,234,220,473,202,248,232,221,474,203,249,233,222,475,204,679,680,678,677,479,283,258,22,272,480,273,284,256,23,481,271,285,257,21,282,478,268,261,18,280,476,269,259,19,281,477,270,260,20,485,274,263,253,13,264,275,254,486,14,262,276,255,487,12,277,266,252,484,16,278,267,250,482,17,279,265,251,483,15,692,691,690,689,536,142,314,304,137,537,138,143,315,305,538,136,144,313,306,145,539,140,310,307,146,540,141,311,308,147,541,139,312,309,542,148,135,320,302,133,149,321,543,303,134,150,319,544,301,151,131,316,545,298,152,132,317,546,299,153,130,318,547,300,699,700,698,697,68,96,119,108,82,69,80,97,120,109,70,81,95,121,107,92,71,85,118,104,93,72,83,116,105,94,73,84,117,106,74,102,88,125,114,86,103,126,75,115,87,101,127,76,113,98,91,124,77,110,99,89,122,78,111,100,90,123,79,112,663,664,662,661,165,380,620,615,634,163,632,381,621,616,164,633,382,622,614,383,161,637,623,618,384,162,635,624,619,385,160,636,625,617,156,386,640,626,613,638,387,627,154,611,639,388,628,155,612,389,643,629,159,609,390,641,630,157,610,391,642,631,158,608,682,683,684,681,552,659,658,657,656,553,649,651,650,648,551,652,655,654,653,343,548,128,329,31,646,549,645,644,647,342,550,129,328,30,558,338,331,327,26,332,336,325,559,24,330,337,326,557,25,341,334,323,554,29,339,335,324,555,27,340,333,322,556,28,695,696,693,694,289,515,491,526,502,290,500,516,492,524,291,501,517,493,525,514,288,505,490,529,512,286,503,488,527,513,287,504,489,528,295,521,508,497,532,506,522,498,296,530,507,523,499,297,531,520,511,496,294,535,518,509,494,292,533,519,510,495,293,534,667,668,665,666,172,404,439,417,392,173,393,405,437,418,174,394,406,438,416,407,175,395,435,420,408,176,396,436,421,409,177,397,434,419,170,410,398,430,423,399,411,428,171,424,400,412,429,169,422,413,401,433,166,426,414,402,431,167,427,415,403,432,168,425,675,676,673,674 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#ea8bb88472b4cb0aad957f1394df72437c069594286fecb60b6451f1d57bec9b, 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 21:20:33 · history