Equation 677 Database

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Magma 21629d124918…

magma 21629d124918
Size
705
Isomorphism class hash
21629d12491851853ac3599cd5c1fe807aaadae05331663fdad35f130948a4b8
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 21:53:16
Display reorder
660,312,332,349,115,315,313,116,330,350,316,331,114,314,348,317,311,328,118,345,318,309,329,119,346,319,310,327,117,347,320,338,340,303,113,321,336,341,304,111,322,337,339,305,112,323,343,334,306,109,324,344,335,307,110,325,342,333,308,108,326,685,686,688,687,420,392,410,222,378,421,223,390,408,379,391,224,422,409,380,419,388,221,406,377,417,389,219,407,375,418,387,220,405,376,398,401,411,228,384,396,399,412,229,385,397,400,413,230,386,404,394,414,227,383,402,395,415,225,381,403,393,416,226,382,701,702,704,703,559,587,599,294,566,560,295,585,597,564,586,296,558,598,565,562,583,293,595,569,563,584,291,596,567,561,582,292,594,568,578,590,557,300,572,576,588,555,301,570,577,589,556,302,571,593,581,553,299,575,591,579,554,297,573,592,580,552,298,574,670,669,672,671,241,62,431,84,56,242,85,60,429,54,61,86,240,430,55,237,65,87,434,59,238,63,88,432,57,239,64,89,433,58,68,426,232,90,51,66,427,233,91,52,67,428,231,92,53,425,71,235,93,50,423,69,236,94,48,424,70,234,95,49,680,677,679,678,442,98,23,34,243,443,35,96,21,244,97,33,441,22,245,445,101,30,19,246,446,99,31,20,247,444,100,32,18,248,104,14,440,25,249,102,12,438,26,250,103,13,439,24,251,17,107,436,28,252,15,105,437,29,253,16,106,435,27,254,689,690,691,692,500,519,535,271,516,498,272,520,536,517,521,270,499,534,518,496,522,267,531,515,497,523,268,532,513,495,524,269,533,514,525,541,506,277,507,526,542,504,278,508,527,540,505,276,509,537,528,502,273,510,538,529,503,274,511,539,530,501,275,512,697,698,700,699,607,635,647,130,614,608,131,633,645,612,634,129,606,646,613,610,631,126,643,617,611,632,127,644,615,609,630,128,642,616,626,638,605,121,620,624,636,603,122,618,625,637,604,120,619,641,629,601,124,623,639,627,602,125,621,640,628,600,123,622,661,662,664,663,182,197,358,170,192,180,168,195,359,193,196,169,181,357,194,178,200,166,361,191,179,198,167,362,189,177,199,165,360,190,203,356,173,161,183,201,354,171,159,184,202,355,172,160,185,352,206,176,164,186,353,204,174,162,187,351,205,175,163,188,682,681,684,683,140,547,153,287,147,138,285,548,154,148,546,286,139,155,149,136,550,290,156,146,137,551,288,157,144,135,549,289,158,145,655,654,653,282,652,659,658,657,283,656,650,649,648,284,651,132,544,142,281,152,133,545,143,279,150,134,543,141,280,151,693,694,696,695,476,454,460,257,492,474,255,455,461,493,453,256,475,459,494,472,457,260,463,491,473,458,258,464,489,471,456,259,462,490,452,466,482,263,483,450,467,480,261,484,451,465,481,262,485,469,448,478,266,486,470,449,479,264,487,468,447,477,265,488,666,665,668,667,8,79,44,368,215,6,366,80,42,213,78,367,7,43,214,11,82,364,47,218,9,83,365,45,216,10,81,363,46,217,77,39,3,374,210,75,40,4,372,211,76,41,5,373,212,38,73,2,370,209,36,74,1,371,207,37,72,0,369,208,674,673,676,675 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#fb895e2582be84c8b2721db1499636a6dec5ebe66e3b80b47964e64d8130d57b, 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 21:53:17 · history