Equation 677 Database

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Magma 3f5bd012a8ec…

magma 3f5bd012a8ec
Size
705
Isomorphism class hash
3f5bd012a8ec60dc3fff70f8463df7948fbc702366221cc578ae838bb9e3574e
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 16:34:27
Display reorder
660,146,553,550,558,555,144,573,570,578,575,145,593,590,598,595,613,149,610,618,615,633,147,630,638,635,653,148,650,658,655,152,513,510,518,515,150,533,530,538,535,151,493,490,498,495,426,155,423,429,427,452,153,449,456,454,472,154,469,476,474,698,694,692,690,289,541,549,551,552,290,561,569,571,572,288,581,589,591,592,601,292,609,611,612,620,293,629,631,632,640,291,649,651,652,295,502,509,511,512,296,522,529,531,532,294,482,489,491,492,430,298,435,424,425,441,299,448,450,451,461,297,468,470,471,702,689,696,687,119,74,85,271,366,117,72,86,272,367,118,73,84,270,368,77,115,88,274,369,75,116,89,275,370,76,114,87,273,371,110,80,91,269,364,108,78,92,267,365,109,79,90,268,363,83,113,94,265,360,81,111,95,266,361,82,112,93,264,362,668,670,672,681,177,354,198,325,402,178,355,199,326,403,179,356,200,324,404,357,176,201,328,405,358,174,202,329,406,359,175,203,327,407,168,352,196,331,400,169,353,197,332,401,170,351,195,330,399,348,171,192,334,396,349,172,193,335,397,350,173,194,333,398,682,675,667,677,125,557,544,543,542,123,577,564,563,562,124,597,584,583,582,617,121,604,603,602,637,122,624,623,622,657,120,644,643,642,131,517,505,504,503,129,537,525,524,523,130,497,485,484,483,428,127,420,432,431,455,128,444,443,442,475,126,464,463,462,704,695,697,699,133,554,547,546,559,134,574,567,566,579,132,594,587,586,599,614,136,607,606,619,634,137,627,626,639,654,135,647,646,659,139,514,507,506,519,140,534,527,526,539,138,494,487,486,499,436,142,434,433,437,453,143,446,445,457,473,141,466,465,477,688,701,693,703,54,556,540,548,545,55,576,560,568,565,56,596,580,588,585,616,57,600,608,605,636,58,621,628,625,656,59,641,648,645,52,516,501,508,500,53,536,521,528,520,51,496,480,488,481,438,48,439,422,421,459,49,458,447,440,478,50,479,467,460,685,700,691,686,279,6,306,28,104,280,7,307,29,102,281,8,308,27,103,9,278,309,24,107,10,276,310,25,105,11,277,311,26,106,285,4,304,34,99,286,5,305,35,100,287,3,303,33,101,1,284,300,30,98,0,282,301,31,96,2,283,302,32,97,676,674,669,664,164,181,12,211,342,162,182,13,212,343,163,180,14,210,344,184,167,15,214,345,185,165,16,215,346,183,166,17,213,347,159,187,18,209,340,160,188,19,207,341,161,186,20,208,339,190,158,21,205,336,191,156,22,206,337,189,157,23,204,338,684,666,679,663,68,390,231,258,46,66,391,232,259,47,67,392,233,260,45,393,71,230,261,42,394,69,228,262,43,395,70,229,263,44,63,388,237,256,37,64,389,238,257,38,65,387,239,255,36,384,62,236,252,40,385,60,234,253,41,386,61,235,254,39,661,683,673,678,249,318,378,224,414,250,319,379,222,415,251,320,380,223,416,321,248,381,227,417,322,246,382,225,418,323,247,383,226,419,240,316,376,219,412,241,317,377,220,413,242,315,375,221,411,312,243,372,218,408,313,244,373,216,409,314,245,374,217,410,662,680,665,671 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#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 16:34:28 · history