Equation 677 Database

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Magma 79e4b25f4ff9…

magma 79e4b25f4ff9
Size
705
Isomorphism class hash
79e4b25f4ff99199591ce0612d6bf1a16c4f2d975471fb9082dc3888fe90989d
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 19:50:50
Display reorder
660,564,540,366,552,577,565,541,578,367,553,566,542,576,368,554,543,567,580,369,555,544,568,581,370,556,545,569,579,371,557,583,546,372,570,558,584,547,373,571,559,582,548,374,572,560,549,586,375,573,561,550,587,376,574,562,551,585,377,575,563,687,688,686,685,95,116,405,130,164,93,114,162,406,131,94,115,163,407,129,119,91,167,404,126,117,92,165,402,127,118,90,166,403,128,159,111,411,86,121,160,112,412,84,122,161,113,413,85,120,110,158,410,89,124,108,156,408,87,125,109,157,409,88,123,703,704,701,702,535,186,361,37,24,536,187,25,362,38,534,188,26,360,36,189,538,27,364,40,190,539,28,365,41,191,537,29,363,39,30,184,359,533,43,31,185,357,531,44,32,183,358,532,42,180,33,355,529,46,181,34,356,530,47,182,35,354,528,45,671,672,670,669,426,450,74,415,439,427,451,440,72,416,428,452,438,73,414,453,429,442,77,418,454,430,443,75,419,455,431,441,76,417,445,456,80,432,421,446,457,78,433,422,444,458,79,434,420,459,448,83,435,424,460,449,81,436,425,461,447,82,437,423,679,680,678,677,279,258,469,275,54,280,259,55,470,273,281,260,56,468,274,261,278,57,472,271,262,276,58,473,272,263,277,59,471,270,52,256,467,285,266,53,257,465,286,264,51,255,466,287,265,252,48,463,284,269,253,49,464,282,267,254,50,462,283,268,692,691,690,689,307,327,513,340,322,308,328,323,514,341,306,329,321,515,339,326,310,318,512,336,324,311,319,510,337,325,309,320,511,338,313,333,519,305,346,314,334,520,303,347,312,335,521,304,345,332,316,518,301,342,330,317,516,302,343,331,315,517,300,344,699,700,698,697,216,241,197,205,229,217,242,230,195,206,218,240,228,196,204,244,219,232,193,208,245,220,233,194,209,243,221,231,192,207,235,247,203,222,211,236,248,201,223,212,234,246,202,224,210,250,238,199,225,214,251,239,200,226,215,249,237,198,227,213,663,664,662,661,613,588,380,600,626,614,589,624,378,601,612,590,625,379,602,591,616,629,383,603,592,617,627,381,604,593,615,628,382,605,632,594,386,619,606,630,595,384,620,607,631,596,385,618,608,597,635,389,622,609,598,633,387,623,610,599,634,388,621,611,682,683,684,681,649,648,16,650,651,653,652,655,17,654,656,657,659,15,658,645,646,647,12,644,636,637,638,13,639,641,642,643,14,640,527,172,22,178,353,525,173,23,179,351,526,171,21,177,352,168,523,18,174,349,169,524,19,175,350,170,522,20,176,348,695,696,693,694,497,65,291,481,503,495,63,501,292,482,496,64,502,293,480,61,493,499,290,484,62,494,500,288,485,60,492,498,289,483,509,71,297,488,479,507,69,298,486,477,508,70,299,487,478,67,505,296,491,475,68,506,294,489,476,66,504,295,490,474,667,668,665,666,398,138,107,155,8,396,139,6,105,153,397,140,7,106,154,141,401,11,103,151,142,399,9,104,152,143,400,10,102,150,3,136,98,393,146,4,137,96,394,144,5,135,97,395,145,132,2,101,392,149,133,1,99,390,147,134,0,100,391,148,675,676,673,674 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#b24873ef385d9876d07add1b0ccd1e5b9965acff1b69e8225210d446f480d74b, 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 19:50:51 · history