Equation 677 Database

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Magma 7690ea95a3b4…

magma 7690ea95a3b4
Size
705
Isomorphism class hash
7690ea95a3b49d7fe0ce9c3771ab85d0dc114d389a2ac28e811e0ce9eb885315
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 16:34:11
Display reorder
660,407,606,618,629,594,408,604,616,630,592,409,605,617,628,593,609,406,621,632,597,607,404,619,633,595,608,405,620,631,596,413,612,624,635,600,414,610,622,636,598,415,611,623,634,599,615,412,627,638,603,613,410,625,639,601,614,411,626,637,602,687,688,686,685,466,260,275,280,21,464,258,273,281,22,465,259,274,279,23,263,469,271,276,20,261,467,272,277,18,262,468,270,278,19,472,255,266,286,12,470,256,264,287,13,471,257,265,285,14,254,475,269,282,15,252,473,267,283,16,253,474,268,284,17,703,704,701,702,8,383,402,162,588,6,384,403,163,586,7,385,401,164,587,382,11,398,165,591,380,9,399,166,589,381,10,400,167,590,3,389,393,160,583,4,390,394,161,584,5,391,392,159,585,388,2,396,156,582,386,1,397,157,580,387,0,395,158,581,671,672,670,669,169,296,484,499,503,170,294,482,497,504,168,295,483,498,505,299,172,487,495,502,297,173,485,496,500,298,171,486,494,501,175,291,479,490,509,176,292,480,488,510,174,293,481,489,511,290,178,478,493,508,288,179,476,491,506,289,177,477,492,507,679,680,678,677,311,520,533,186,117,309,518,534,187,118,310,519,535,188,119,523,307,532,189,116,521,308,530,190,114,522,306,531,191,115,302,515,524,184,108,300,516,525,185,109,301,517,526,183,110,514,305,527,180,111,512,303,528,181,112,513,304,529,182,113,692,691,690,689,206,129,37,354,554,204,130,38,355,555,205,131,36,356,556,128,209,40,357,557,126,207,41,358,558,127,208,39,359,559,212,120,43,352,552,210,121,44,353,553,211,122,42,351,551,123,215,46,348,548,124,213,47,349,549,125,214,45,350,550,699,700,698,697,57,93,99,63,82,58,94,100,64,83,59,95,101,65,81,92,56,98,62,78,90,54,96,60,79,91,55,97,61,80,48,84,105,69,73,49,85,106,70,74,50,86,107,71,72,87,51,104,68,76,88,52,102,66,77,89,53,103,67,75,663,664,662,661,642,230,134,422,218,640,228,132,423,216,641,229,133,424,217,233,645,137,425,221,231,643,135,426,219,232,644,136,427,220,648,236,140,420,224,646,234,138,421,222,647,235,139,419,223,239,651,143,416,227,237,649,141,417,225,238,650,142,418,226,682,683,684,681,24,377,571,567,367,25,378,572,568,368,26,376,570,566,366,375,27,573,569,379,653,28,654,652,655,656,29,659,658,657,30,370,575,565,365,31,371,576,563,363,32,369,574,564,364,373,33,578,561,361,374,34,579,562,362,372,35,577,560,360,695,696,693,694,540,319,325,340,194,541,320,326,341,192,539,318,324,339,193,322,536,328,336,197,323,537,329,337,195,321,538,327,338,196,546,317,331,346,200,547,315,332,347,198,545,316,330,345,199,313,542,334,342,203,314,543,335,343,201,312,544,333,344,202,667,668,665,666,246,451,457,150,436,247,449,455,151,434,248,450,456,152,435,447,249,453,153,439,448,250,454,154,437,446,251,452,155,438,244,442,463,148,431,245,440,461,149,432,243,441,462,147,433,445,240,459,144,430,443,241,460,145,428,444,242,458,146,429,675,676,673,674 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#357eb5a07f294d712e4efb5d2eb529ba387854e51bbe679ac1cbb62e1e3b2fae, 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 16:34:13 · history