Equation 677 Database

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Magma 5def845ecc28…

magma 5def845ecc28
Size
705
Isomorphism class hash
5def845ecc28ce659caf8533455fb2b22f19237d008ff210f2925ce8bd7e2e37
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 21:16:22
Display reorder
660,572,597,332,584,560,573,598,561,333,585,574,596,562,334,586,575,600,563,335,587,576,601,564,336,588,577,599,565,337,589,566,578,338,603,590,567,579,339,604,591,568,580,340,602,592,581,569,341,606,593,582,570,342,607,594,583,571,343,605,595,687,688,686,685,404,428,221,416,392,405,429,393,219,417,406,430,394,220,418,407,431,395,224,419,408,432,396,222,420,409,433,397,223,421,398,410,227,434,422,399,411,225,435,423,400,412,226,436,424,413,401,230,437,425,414,402,228,438,426,415,403,229,439,427,703,704,701,702,32,195,327,556,170,30,196,168,328,554,31,197,169,326,555,35,198,166,330,559,33,199,167,331,557,34,200,165,329,558,161,27,325,201,551,159,28,323,202,552,160,29,324,203,553,26,164,321,204,550,24,162,322,205,548,25,163,320,206,549,671,672,670,669,244,7,69,177,448,245,8,446,67,178,243,6,447,68,179,247,10,451,65,180,248,11,449,66,181,246,9,450,64,182,443,250,75,5,175,444,251,73,3,176,445,249,74,4,174,253,442,71,0,171,254,440,72,2,172,252,441,70,1,173,679,680,678,677,127,458,18,261,473,128,459,474,19,262,129,460,475,20,263,126,461,472,21,264,124,462,470,22,265,125,463,471,23,266,464,133,16,456,259,465,134,17,457,260,466,135,15,455,258,132,467,12,452,255,130,468,13,453,256,131,469,14,454,257,692,691,690,689,82,139,191,287,532,83,140,530,189,285,84,141,531,190,286,85,138,535,194,290,86,136,533,192,288,87,137,534,193,289,527,80,186,145,282,528,81,187,146,283,529,79,188,147,284,76,526,185,144,281,77,524,183,142,279,78,525,184,143,280,699,700,698,697,96,117,51,111,47,94,115,45,52,109,95,116,46,53,110,99,113,43,50,107,97,114,44,48,108,98,112,42,49,106,38,91,57,123,102,36,92,58,121,100,37,93,59,122,101,90,41,56,119,105,88,39,54,120,103,89,40,55,118,104,663,664,662,661,609,635,346,625,646,610,636,644,344,623,608,637,645,345,624,612,634,649,349,621,613,632,647,347,622,611,633,648,348,620,652,615,352,641,631,650,616,350,642,629,651,614,351,643,630,618,655,355,640,627,619,653,353,638,628,617,654,354,639,626,682,683,684,681,298,61,537,150,310,299,62,311,538,151,297,63,309,536,152,301,60,313,540,149,656,657,658,541,659,300,302,312,539,148,315,296,543,303,156,316,294,544,304,157,314,295,542,305,158,292,318,546,306,155,293,319,547,307,153,291,317,545,308,154,695,696,693,694,505,481,269,515,493,503,479,491,267,516,504,480,492,268,517,501,477,489,272,514,502,478,490,270,512,500,476,488,271,513,499,511,275,487,521,497,509,273,485,522,498,510,274,486,523,507,495,278,483,520,508,496,276,484,518,506,494,277,482,519,667,668,665,666,389,364,235,212,378,390,362,379,236,210,391,363,377,234,211,388,367,374,231,208,386,365,375,232,209,387,366,376,233,207,369,380,241,359,218,370,381,242,360,216,368,382,240,361,217,383,372,237,358,214,384,373,238,356,215,385,371,239,357,213,675,676,673,674 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#e2a478bba1a9cde7c476f091d01301457f542f6a1b857d9784efc8df77c998e9, 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 21:16:23 · history