Equation 677 Database

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Magma 2579e0661bfc…

magma 2579e0661bfc
Size
705
Isomorphism class hash
2579e0661bfc4aed88fdc23de56f24e0e1474ed67016c7a5208af84a5903f907
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 16:24:55
Display reorder
704,51,98,90,79,52,96,91,80,97,53,92,78,50,101,93,82,48,99,94,83,49,100,95,81,57,104,88,77,58,102,89,75,59,103,87,76,56,107,84,73,54,105,85,74,55,106,86,72,67,68,66,70,71,69,65,63,60,61,62,64,700,701,703,702,658,657,659,656,650,648,651,649,652,653,654,655,642,640,643,641,646,645,647,644,638,636,639,637,620,621,623,622,612,613,615,614,616,617,619,618,633,632,635,634,624,625,627,626,629,628,631,630,130,131,129,126,127,128,121,122,123,124,125,120,691,689,690,688,259,313,359,346,260,314,357,347,312,258,358,345,262,316,355,342,263,317,356,343,261,315,354,344,257,319,350,337,255,320,348,338,256,318,349,336,253,322,353,340,254,323,351,341,252,321,352,339,334,335,333,330,331,332,325,326,327,328,329,324,675,672,674,673,135,216,210,200,136,217,211,198,218,137,212,199,134,219,213,203,132,220,214,201,133,221,215,202,141,222,208,195,142,223,209,196,143,224,207,197,140,225,204,194,138,226,205,192,139,227,206,193,237,238,239,236,234,235,228,229,233,231,232,230,681,683,680,682,116,416,445,432,114,414,446,433,415,115,444,434,119,419,448,435,117,417,449,436,118,418,447,437,111,411,451,438,112,412,452,439,113,413,450,440,110,410,454,441,108,408,455,442,109,409,453,443,421,422,420,424,425,423,427,428,429,430,431,426,693,692,694,695,24,159,153,188,25,160,154,186,161,26,155,187,27,158,152,191,28,156,150,189,29,157,151,190,30,165,144,183,31,166,145,184,32,167,146,185,33,164,147,182,34,162,148,180,35,163,149,181,175,176,174,178,179,177,173,171,168,169,170,172,698,697,699,696,38,560,588,578,36,558,589,576,559,37,590,577,41,563,591,581,39,561,592,579,40,562,593,580,44,555,594,584,42,556,595,582,43,557,596,583,47,554,597,587,45,552,598,585,46,553,599,586,566,564,565,569,567,568,572,570,574,575,573,571,686,684,687,685,13,360,406,393,14,361,407,394,362,12,405,395,16,363,402,392,17,364,403,390,15,365,404,391,19,366,397,384,20,367,398,385,18,368,396,386,22,369,400,387,23,370,401,388,21,371,399,389,381,382,383,380,378,379,372,373,377,375,376,374,661,663,660,662,247,266,311,299,248,264,309,297,265,246,310,298,250,269,307,295,251,267,308,296,249,268,306,294,245,272,302,290,243,270,300,288,244,271,301,289,241,275,305,293,242,273,303,291,240,274,304,292,287,285,286,283,284,282,278,276,280,281,279,277,676,678,677,679,8,482,476,463,6,480,474,464,481,7,475,462,11,485,479,466,9,483,477,467,10,484,478,465,3,488,471,461,4,486,472,459,5,487,473,460,2,491,470,457,1,489,468,458,0,490,469,456,502,503,501,498,499,500,493,494,495,496,497,492,665,667,664,666,604,519,515,548,605,520,513,546,521,603,514,547,600,518,511,551,601,516,512,549,602,517,510,550,610,525,506,543,611,526,504,544,609,527,505,545,606,524,509,542,607,522,507,540,608,523,508,541,535,536,534,538,539,537,533,531,528,529,530,532,670,671,669,668 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#3180ad8dfd10ba7152583c35a71774bceecf2852df6e850dd8c0dada693f6036, 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 16:24:56 · history