Equation 677 Database

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Magma 4475eecdb6f8…

magma 4475eecdb6f8
Size
705
Isomorphism class hash
4475eecdb6f8fd7fa1f9ffd9dcea54fc441b4af45aedf7be7cf8b951333d951d
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 20:32:44
Display reorder
660,82,367,68,386,376,83,368,66,384,377,81,366,385,375,67,370,78,71,389,372,371,79,69,387,373,369,80,70,388,374,365,73,63,392,382,363,74,64,390,383,391,364,72,65,381,361,76,62,395,378,362,77,60,393,379,360,75,61,394,380,685,686,688,687,442,126,170,428,133,443,127,168,426,134,441,128,427,132,169,129,438,173,431,136,130,439,171,429,137,131,440,172,430,135,124,433,176,423,139,125,434,174,424,140,425,123,432,175,138,120,436,179,422,142,121,437,177,420,143,122,435,178,421,141,701,702,704,703,554,569,357,599,576,552,567,358,597,577,553,568,598,578,359,565,557,356,595,579,566,555,354,596,580,564,556,355,594,581,575,560,348,590,582,573,558,349,588,583,589,574,559,350,584,571,563,351,593,585,572,561,352,591,586,570,562,353,592,587,670,669,672,671,450,456,36,5,478,451,457,37,3,479,452,458,4,477,38,459,453,39,0,474,460,454,40,2,475,461,455,41,1,476,462,448,42,11,469,463,449,43,9,470,10,464,447,44,468,465,444,45,7,472,466,445,46,8,473,467,446,47,6,471,680,677,679,678,270,486,52,508,494,271,487,53,509,492,272,488,507,493,51,489,273,48,504,497,490,274,49,505,495,491,275,50,506,496,484,276,58,514,500,485,277,59,515,498,513,483,278,57,499,480,279,54,510,503,481,280,55,511,501,482,281,56,512,502,689,690,691,692,259,26,537,250,338,260,24,538,251,336,258,25,249,337,539,29,262,536,246,341,27,263,534,247,339,28,261,535,248,340,21,265,528,256,333,22,266,529,257,334,255,23,264,530,335,20,268,531,252,332,18,269,532,253,330,19,267,533,254,331,697,698,700,699,606,612,635,101,95,607,613,633,99,93,608,614,100,94,634,615,609,631,97,91,616,610,632,98,92,617,611,630,96,90,618,604,626,107,86,619,605,624,105,84,106,620,603,625,85,621,600,629,103,89,622,601,627,104,87,623,602,628,102,88,661,662,664,663,183,205,398,222,214,184,206,396,223,215,185,204,224,213,397,208,182,401,225,210,209,180,399,226,211,207,181,400,227,212,203,189,404,228,220,201,190,402,229,221,230,202,191,403,219,199,188,407,231,216,200,186,405,232,217,198,187,406,233,218,682,681,684,683,35,15,545,342,195,33,16,543,343,196,34,17,344,197,544,14,31,541,345,194,12,32,542,346,192,13,30,540,347,193,641,642,551,643,640,645,646,549,647,644,638,636,637,550,639,652,654,547,655,653,657,658,548,659,656,648,650,546,651,649,693,694,696,695,299,308,522,284,322,297,306,523,282,323,298,307,283,321,524,311,295,525,287,318,309,296,526,285,319,310,294,527,286,320,314,305,520,290,328,312,303,521,288,329,289,313,304,519,327,317,301,516,293,324,315,302,517,291,325,316,300,518,292,326,666,665,668,667,111,414,234,156,150,112,415,235,157,151,113,416,158,152,236,417,110,237,159,153,418,108,238,160,154,419,109,239,161,155,412,117,240,162,148,413,118,241,163,149,164,411,119,242,147,408,116,243,165,144,409,114,244,166,145,410,115,245,167,146,674,673,676,675 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#bf96e9533ef77c4b1918ac824d690467af6cf34f1d8a49dfc9562b509f0b1543, 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 20:32:45 · history