Equation 677 Database

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Magma 4edcd7efe4ec…

magma 4edcd7efe4ec
Size
705
Isomorphism class hash
4edcd7efe4ecaa11dfe39369aabc2ccae5a19e900d8bc9988763efe10158e42f
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 18:19:09
Display reorder
660,362,108,365,380,343,363,109,366,381,344,379,107,361,364,345,358,104,368,376,342,359,105,369,377,340,360,106,367,378,341,114,371,353,386,349,115,372,354,387,350,113,370,352,385,351,374,110,356,382,348,375,111,357,383,346,373,112,355,384,347,685,686,688,687,484,184,449,463,482,485,182,450,464,483,465,183,486,448,481,487,187,452,462,478,488,185,453,460,479,489,186,451,461,480,179,455,490,469,473,180,456,491,470,474,181,454,492,471,472,458,178,493,468,476,459,176,494,466,477,457,177,495,467,475,701,702,704,703,612,102,627,339,9,610,103,625,337,7,338,101,611,626,8,615,98,623,335,12,613,99,624,336,10,614,100,622,334,11,93,618,607,330,4,94,616,608,328,5,92,617,609,329,6,621,96,606,333,3,619,97,604,331,0,620,95,605,332,2,670,669,672,671,519,195,522,239,504,517,196,520,240,502,241,194,518,521,503,515,198,525,238,507,516,199,523,236,505,514,197,524,237,506,193,528,510,245,499,191,526,508,246,500,192,527,509,247,501,531,189,513,244,498,529,190,511,242,496,530,188,512,243,497,680,677,679,678,207,543,256,271,272,208,541,254,269,273,270,542,206,255,274,210,539,259,267,275,211,540,257,268,276,209,538,258,266,277,534,251,205,262,278,532,252,203,260,279,533,253,204,261,280,250,537,201,265,281,248,535,202,263,282,249,536,200,264,283,689,690,691,692,574,149,584,304,70,575,150,585,302,71,303,151,576,583,72,577,148,580,307,69,578,146,581,305,67,579,147,582,306,68,140,590,572,299,61,141,591,573,300,62,142,589,571,301,63,586,143,568,298,64,587,144,569,296,65,588,145,570,297,66,697,698,700,699,636,32,651,37,13,634,33,649,38,14,39,31,635,650,15,639,35,647,40,16,637,36,648,41,17,638,34,646,42,18,30,642,631,43,19,28,640,632,44,20,29,641,633,45,21,645,26,630,46,22,643,27,628,47,23,644,25,629,48,24,661,662,664,663,414,123,152,396,410,412,124,153,394,411,395,122,413,154,409,417,126,155,399,406,415,127,156,397,407,416,125,157,398,408,121,158,420,391,401,119,159,418,392,402,120,160,419,393,400,161,117,423,390,404,162,118,421,388,405,163,116,422,389,403,682,681,684,683,318,599,78,89,313,319,600,76,90,314,91,598,320,77,312,321,602,74,88,316,322,603,75,86,317,323,601,73,87,315,597,657,659,656,658,595,82,324,1,308,596,652,654,653,655,80,593,325,83,311,81,594,326,84,309,79,592,327,85,310,693,694,696,695,560,286,221,233,550,561,284,222,234,551,235,285,559,223,552,556,289,220,232,553,557,287,218,230,554,558,288,219,231,555,292,212,566,224,548,290,213,567,225,549,291,214,565,226,547,215,295,562,227,544,216,293,563,228,545,217,294,564,229,546,666,665,668,667,59,165,431,436,128,60,166,432,437,129,438,164,58,430,130,55,168,434,439,131,56,169,435,440,132,57,167,433,441,133,171,429,50,442,134,172,427,51,443,135,170,428,49,444,136,425,174,53,445,137,426,175,54,446,138,424,173,52,447,139,674,673,676,675 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#7b2d22e166b1ff02dad840b7a1389a143f850a338adb3bda964b6fc81ff7fb8b, 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 18:19:10 · history