Equation 677 Database

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Magma 7e661a417986…

magma 7e661a417986
Size
705
Isomorphism class hash
7e661a4179865cb62681c2305c8c7a2a04a05552bb60102afcd8c057c2091299
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 17:32:47
Display reorder
660,271,449,632,42,443,633,272,40,441,447,634,448,273,41,442,270,635,452,45,446,636,268,450,43,444,637,269,451,44,445,638,277,455,48,438,639,278,453,46,439,640,279,454,47,440,276,641,458,51,437,274,642,456,49,435,50,275,643,457,436,687,688,686,685,133,323,219,515,123,217,134,513,121,324,218,322,135,514,122,132,215,326,518,119,216,130,327,516,120,214,131,325,517,118,210,124,321,510,114,208,125,319,511,112,209,126,320,512,113,127,213,317,509,117,128,211,318,507,115,508,129,212,316,116,703,704,701,702,256,252,423,627,186,424,257,628,184,250,425,251,258,626,185,259,426,255,630,189,427,260,253,631,187,428,261,254,629,188,429,262,247,625,192,430,263,248,623,190,431,264,249,624,191,265,432,246,621,195,266,433,244,622,193,620,267,434,245,194,671,672,670,669,207,527,330,142,6,328,205,143,7,525,329,526,206,144,8,203,333,530,145,9,331,204,528,146,10,332,202,529,147,11,336,198,522,140,4,334,196,523,141,5,335,197,524,139,3,201,339,521,136,1,199,337,519,137,0,138,200,338,520,2,679,680,678,677,544,539,150,564,343,148,545,565,344,537,149,538,543,566,345,547,153,542,563,342,151,548,540,561,340,152,546,541,562,341,156,550,534,555,349,154,551,535,556,350,155,549,536,557,351,553,159,533,558,348,554,157,531,559,346,560,552,158,532,347,692,691,690,689,406,29,169,24,585,170,407,22,586,30,171,28,408,23,587,409,168,32,27,588,166,410,33,25,589,167,411,31,26,590,160,404,35,19,583,161,405,36,20,584,162,403,34,21,582,400,163,38,18,579,401,164,39,16,580,17,402,165,37,581,699,700,698,697,86,68,104,88,52,105,87,89,53,69,103,67,85,90,54,82,100,64,91,55,101,83,65,92,56,102,84,66,93,57,110,77,74,94,58,111,78,75,95,59,109,76,73,96,60,80,106,70,97,61,81,107,71,98,62,99,79,108,72,63,663,664,662,661,472,467,646,492,286,644,473,493,287,465,645,466,471,494,288,475,649,470,491,289,647,476,468,489,290,648,474,469,490,291,652,478,462,483,284,650,479,463,484,285,651,477,464,485,283,481,655,461,486,280,482,653,459,487,281,488,480,654,460,282,682,683,684,681,14,598,172,612,416,173,15,613,414,599,174,597,13,611,415,12,175,601,609,412,176,657,656,658,659,177,602,600,610,413,178,603,596,618,422,179,604,594,619,420,180,605,595,617,421,606,181,592,614,418,607,182,593,615,419,616,608,183,591,417,695,696,693,694,375,363,571,385,391,572,373,386,392,361,570,362,374,387,393,371,567,359,384,390,568,372,360,382,388,569,370,358,383,389,577,366,354,376,397,578,364,352,377,398,576,365,353,378,399,369,573,357,379,396,367,574,355,380,394,381,368,575,356,395,667,668,665,666,233,226,506,298,306,504,234,299,304,227,505,228,232,300,305,236,502,229,301,309,503,237,230,302,307,501,235,231,303,308,497,239,224,296,312,495,240,225,297,310,496,238,223,295,311,242,500,220,292,315,243,498,221,293,313,294,241,499,222,314,675,676,673,674 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#58acf36cbe6044882516075a72a3c87dd19ad7333778c9b60a583a8d5c85fb41, 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 17:32:48 · history