Equation 677 Database

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Magma 3bfe7df4eea6…

magma 3bfe7df4eea6
Size
705
Isomorphism class hash
3bfe7df4eea6e0cd9bd54023576a171a108c132f2b65d18a6ee68e2f6795ed75
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 20:09:07
Display reorder
660,276,264,102,289,252,265,103,287,277,253,263,104,275,251,288,101,260,285,272,248,99,261,286,273,249,100,262,284,274,250,270,93,295,282,258,271,94,293,283,259,269,95,294,281,257,96,266,291,278,254,97,267,292,279,255,98,268,290,280,256,685,686,688,687,404,403,137,421,388,401,135,419,405,386,402,136,406,387,420,140,399,417,407,391,138,400,418,408,389,139,398,416,409,390,394,132,427,410,383,392,133,425,411,384,393,134,426,412,385,131,397,423,413,382,129,395,424,414,380,130,396,422,415,381,701,702,704,703,562,559,247,582,593,557,245,583,560,594,558,246,561,595,581,243,555,578,565,592,244,556,579,563,590,242,554,580,564,591,550,238,573,568,584,548,236,574,566,585,549,237,572,567,586,241,553,576,571,587,239,551,577,569,588,240,552,575,570,589,670,669,672,671,450,438,146,462,474,439,144,463,451,475,437,145,449,473,461,142,434,458,446,470,143,435,459,447,471,141,436,460,448,472,429,152,453,441,465,430,150,454,442,466,428,151,452,440,464,148,432,456,444,468,149,433,457,445,469,147,431,455,443,467,680,677,679,678,170,158,483,181,193,156,484,182,168,194,157,482,169,192,180,486,154,177,166,189,487,155,178,167,190,485,153,179,165,191,164,481,187,176,199,162,479,188,174,200,163,480,186,175,198,477,160,183,172,195,478,161,184,173,196,476,159,185,171,197,689,690,691,692,89,21,216,34,530,19,217,35,87,531,20,218,88,532,36,215,24,33,92,533,213,22,31,90,534,214,23,32,91,535,16,222,25,84,528,17,223,26,85,529,18,224,27,86,527,221,15,28,83,524,219,13,29,81,525,220,14,30,82,526,697,698,700,699,617,606,655,622,642,607,653,620,618,643,605,654,619,641,621,651,602,625,616,638,652,603,623,614,639,650,604,624,615,640,597,646,628,608,633,598,644,626,609,634,596,645,627,610,632,649,600,631,611,636,647,601,629,612,637,648,599,630,613,635,661,662,664,663,320,319,8,108,304,317,9,109,321,302,318,7,322,303,110,11,315,107,323,307,12,316,105,324,305,10,314,106,325,306,310,6,114,326,299,308,4,115,327,300,309,5,116,328,301,2,313,113,329,298,3,311,111,330,296,0,312,112,331,297,682,681,684,683,59,57,544,40,230,55,542,41,60,231,56,543,58,232,42,547,53,39,62,233,545,54,37,63,234,546,52,38,61,235,48,539,46,64,228,1,540,47,65,229,657,541,656,658,659,538,51,45,67,227,536,49,43,68,225,537,50,44,66,226,693,694,696,695,509,496,211,514,74,494,212,512,510,72,495,210,511,73,513,207,499,517,508,70,208,497,515,506,71,209,498,516,507,69,491,202,520,500,80,492,203,518,501,78,493,201,519,502,79,205,490,523,503,76,206,488,521,504,77,204,489,522,505,75,666,665,668,667,379,366,118,333,346,367,119,334,377,344,365,117,378,345,332,121,362,336,375,349,122,363,337,376,347,120,364,335,374,348,357,124,339,370,352,358,125,340,368,350,356,123,338,369,351,127,360,342,373,355,128,361,343,371,353,126,359,341,372,354,674,673,676,675 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#bc5f623c03e0cf031de7da5cba3786bb6161d1a009770b59759abcaaa846aef4, 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 20:09:08 · history