Equation 677 Database

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Magma 5e4dec0ded00…

magma 5e4dec0ded00
Size
705
Isomorphism class hash
5e4dec0ded00a81d8acc9a59407901b2c0947adcb559c1275af902540b7c5720
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 20:32:57
Display reorder
660,445,455,123,444,443,465,475,124,464,463,421,425,429,428,125,519,505,122,504,503,539,525,120,524,523,499,485,121,484,483,579,565,129,564,563,599,585,130,584,583,544,559,545,131,543,639,625,128,624,623,659,645,126,644,643,619,605,127,604,603,699,691,703,692,447,448,3,454,446,467,468,4,474,466,422,423,435,430,5,508,507,2,516,506,528,527,1,536,526,488,487,0,496,486,568,567,9,576,566,588,587,10,596,586,556,548,547,11,546,628,627,8,636,626,648,647,6,656,646,608,607,7,616,606,695,702,685,688,289,349,213,260,385,290,350,214,258,386,288,348,259,384,215,352,292,212,263,388,353,293,210,261,389,351,291,211,262,387,355,295,204,255,391,356,296,205,256,392,257,354,294,206,390,358,298,207,254,394,359,299,208,252,395,357,297,209,253,393,681,680,675,661,373,337,101,409,95,374,338,99,410,93,372,336,408,94,100,340,376,97,412,91,341,377,98,413,92,339,375,96,411,90,343,379,107,415,86,344,380,105,416,84,414,342,378,106,85,346,382,103,418,89,347,383,104,419,87,345,381,102,417,88,683,665,674,678,452,451,198,458,459,472,471,199,476,477,433,432,438,437,200,512,513,201,514,509,532,533,202,534,529,492,493,203,494,489,572,573,196,574,569,592,593,197,594,589,554,552,553,195,549,632,633,192,634,629,652,653,193,654,649,612,613,194,614,609,693,687,696,686,456,457,66,440,450,478,479,56,460,470,439,436,427,431,61,518,517,81,500,511,538,537,71,520,531,498,497,76,480,491,578,577,39,560,571,598,597,44,581,591,540,558,557,49,551,638,637,36,620,631,658,657,24,640,651,618,617,29,600,611,697,689,701,698,453,441,80,449,442,473,461,69,469,462,434,426,424,420,75,501,515,59,510,502,521,535,64,530,522,481,495,54,490,482,561,575,34,570,562,580,595,25,590,582,550,541,555,31,542,621,635,51,630,622,641,655,41,650,642,601,615,46,610,602,690,704,700,694,361,173,68,285,272,362,171,58,286,270,360,172,287,271,63,169,364,83,284,275,170,365,73,282,273,168,363,78,283,274,179,367,43,276,267,177,368,48,277,268,278,178,366,53,269,175,370,38,279,266,176,371,26,280,264,174,369,33,281,265,670,668,672,676,242,72,35,233,223,240,77,28,231,224,241,82,232,222,30,67,245,50,229,226,57,243,40,230,227,62,244,45,228,225,27,248,65,239,221,32,246,55,237,219,238,37,247,60,220,42,251,79,235,217,47,249,70,236,218,52,250,74,234,216,667,679,677,673,13,325,108,397,136,14,326,109,398,137,12,324,396,135,110,328,16,111,400,132,329,17,112,401,133,327,15,113,399,134,331,19,114,403,142,332,20,115,404,143,402,330,18,116,141,334,22,117,406,138,335,23,118,407,139,333,21,119,405,140,682,662,669,671,144,167,183,301,313,145,165,184,302,314,146,166,300,312,185,163,147,182,304,316,164,148,180,305,317,162,149,181,303,315,158,150,189,307,319,156,151,190,308,320,306,157,152,191,318,161,153,188,310,322,159,154,186,311,323,160,155,187,309,321,663,666,664,684 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#bf96e9533ef77c4b1918ac824d690467af6cf34f1d8a49dfc9562b509f0b1543, 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 20:32:58 · history