Equation 677 Database

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Magma df3ae2523928…

magma df3ae2523928
Size
705
Isomorphism class hash
df3ae25239283ded5561e04719b6625f0dee56105b78b283d706ca9850c3ca0f
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 17:27:18
Display reorder
660,16,392,375,389,405,17,390,376,387,406,377,15,388,407,391,395,12,374,385,404,393,13,372,386,402,394,14,373,384,403,22,398,366,380,411,23,396,367,378,412,21,397,368,379,413,383,401,18,369,410,399,19,370,381,408,400,20,371,382,409,685,686,688,687,189,284,497,500,481,190,282,495,498,482,496,191,499,480,283,287,188,493,503,484,285,186,494,501,485,286,187,492,502,483,195,290,488,506,479,196,288,486,504,477,197,289,487,505,478,509,293,194,491,475,291,192,489,507,476,292,193,490,508,474,701,702,704,703,129,361,611,106,595,130,362,609,107,596,610,131,105,594,360,364,128,607,102,598,365,126,608,103,599,363,127,606,104,597,120,359,602,97,593,121,357,600,98,591,122,358,601,96,592,100,355,123,605,589,356,124,603,101,590,354,125,604,99,588,670,669,672,671,203,298,37,518,86,201,299,41,516,84,36,202,517,85,297,294,199,45,521,89,295,200,47,519,87,296,198,42,520,88,209,304,40,513,92,207,305,38,514,90,208,303,39,515,91,512,300,205,46,95,301,206,43,510,93,302,204,44,511,94,680,677,679,678,211,548,529,545,34,212,546,530,543,30,528,210,544,32,547,551,214,532,541,27,549,215,533,542,29,550,213,531,540,24,217,554,527,536,25,218,552,525,534,26,216,553,526,535,28,539,557,220,523,31,555,221,524,537,33,556,219,522,538,35,689,690,691,692,145,10,341,254,578,146,11,339,252,576,340,144,253,577,9,6,148,337,257,581,7,149,338,255,579,8,147,336,256,580,151,0,332,249,573,152,2,330,250,574,150,1,331,251,575,248,4,154,335,572,5,155,333,246,570,3,153,334,247,571,697,698,700,699,66,51,635,64,619,68,52,633,61,620,634,70,62,618,53,50,65,631,71,622,48,60,632,67,623,49,63,630,69,621,79,57,626,77,617,81,58,624,72,615,82,59,625,74,616,83,56,76,629,613,54,73,627,78,614,55,75,628,80,612,661,662,664,663,263,440,421,437,455,261,438,422,435,453,420,262,436,454,439,443,259,424,433,451,441,260,425,434,452,442,258,423,432,450,269,446,419,428,461,267,444,417,426,459,268,445,418,427,460,431,449,265,415,457,447,266,416,429,458,448,264,414,430,456,682,681,684,683,353,166,157,584,170,351,167,158,582,168,156,352,583,169,165,162,349,160,587,173,163,350,161,585,171,164,348,159,586,172,344,641,640,643,642,342,645,644,647,646,343,637,636,638,639,655,653,347,652,654,657,345,656,659,658,649,346,648,651,650,693,694,696,695,560,236,318,228,312,558,234,319,229,313,320,559,230,314,235,239,563,321,231,315,237,561,322,232,316,238,562,323,233,317,566,242,324,226,310,564,240,325,227,311,565,241,326,225,309,222,245,569,327,306,243,567,328,223,307,244,568,329,224,308,666,665,668,667,473,143,278,182,117,471,141,276,180,118,277,472,181,119,142,139,469,281,185,116,140,470,279,183,114,138,468,280,184,115,464,134,273,177,108,462,132,274,178,109,463,133,275,179,110,176,137,467,272,111,135,465,270,174,112,136,466,271,175,113,674,673,676,675 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#5779f8cee5daac7ffda88b67b379fba3aadfa70634d24364b86a2ac7cf85bc20, 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 17:27:20 · history