Equation 677 Database

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Magma 90056add12db…

magma 90056add12db
Size
705
Isomorphism class hash
90056add12dbf29e9cab95b62f2591742e75c64e98646c267bd717c347d6a8bf
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 16:29:13
Display reorder
660,378,44,370,200,362,379,42,360,371,201,380,43,361,369,199,381,40,365,366,203,382,41,363,367,204,383,39,364,368,202,384,35,357,376,206,33,358,377,385,207,34,359,375,386,205,356,38,372,387,209,354,36,373,388,210,355,37,374,389,208,685,686,688,687,277,135,24,111,446,278,133,444,25,109,279,134,445,26,110,280,138,449,23,114,281,136,447,21,112,282,137,448,22,113,275,130,441,30,106,131,442,31,276,107,132,443,32,274,108,440,129,29,271,105,438,127,27,272,103,439,128,28,273,104,701,702,704,703,344,190,589,563,570,342,191,568,590,564,343,192,569,591,562,347,189,573,588,566,345,187,571,586,567,346,188,572,587,565,350,196,576,580,561,197,574,581,348,559,198,575,582,349,560,579,195,583,353,557,577,193,584,351,558,578,194,585,352,556,670,669,672,671,464,147,457,483,290,462,145,291,458,484,463,146,289,456,485,467,150,293,460,482,465,148,294,461,480,466,149,292,459,481,470,142,288,455,474,143,286,453,468,475,144,287,454,469,476,284,141,451,473,477,285,139,452,471,478,283,140,450,472,479,680,677,679,678,303,497,94,157,79,301,495,80,95,158,302,496,81,96,159,306,493,82,93,160,304,494,83,91,161,305,492,84,92,162,298,488,85,100,155,486,86,101,299,156,487,87,102,300,154,88,491,99,297,151,89,489,97,295,152,90,490,98,296,153,689,690,691,692,539,327,525,63,518,537,325,516,526,64,538,326,517,527,65,535,330,521,524,66,536,328,519,522,67,534,329,520,523,68,545,322,513,531,61,323,514,532,543,62,324,515,533,544,60,512,321,530,541,57,510,319,528,542,58,511,320,529,540,59,697,698,700,699,614,602,651,627,630,615,603,628,649,625,613,601,629,650,626,610,598,633,647,623,611,599,631,648,624,612,600,632,646,622,605,593,636,642,618,594,634,640,606,616,592,635,641,604,617,639,596,645,608,621,637,597,643,609,619,638,595,644,607,620,661,662,664,663,258,392,237,211,227,256,390,228,235,212,257,391,226,236,213,254,395,223,240,214,255,393,224,238,215,253,394,225,239,216,249,398,233,243,217,396,234,241,247,218,397,232,242,248,219,229,401,246,252,220,230,399,244,250,221,231,400,245,251,222,682,681,684,683,8,9,552,333,73,6,10,74,550,331,7,11,75,551,332,4,12,76,555,336,5,13,77,553,334,3,14,78,554,335,657,15,658,659,656,16,72,549,341,337,17,653,654,652,655,70,18,548,2,340,71,19,546,1,338,69,20,547,0,339,693,694,696,695,178,49,163,506,312,179,50,310,164,504,180,48,311,165,505,177,45,308,166,509,175,46,309,167,507,176,47,307,168,508,184,55,318,169,501,56,316,170,185,502,54,317,171,186,503,314,51,172,183,500,315,52,173,181,498,313,53,174,182,499,666,665,668,667,265,116,429,410,417,266,117,418,430,408,267,115,419,431,409,268,119,416,428,413,269,120,414,426,411,270,118,415,427,412,263,122,423,435,405,123,424,436,264,406,121,425,437,262,407,422,125,434,259,404,420,126,432,260,402,421,124,433,261,403,674,673,676,675 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#33fc7ab4b4817466950310b35dd4cd44cb4b00aed5b55945bbae0672c2180aa2, 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 16:29:15 · history