Equation 677 Database

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Magma fca055a07666…

magma fca055a07666
Size
705
Isomorphism class hash
fca055a07666f23271873c5fefab92f83f90625226fce7a0c751b20f90db6d7c
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 17:30:22
Display reorder
660,352,364,387,376,39,353,40,365,388,377,363,41,351,389,375,355,367,42,390,379,356,368,43,391,380,354,366,44,392,378,370,358,37,393,382,371,359,38,394,383,395,369,357,36,381,373,361,33,396,385,374,362,34,397,386,372,360,35,398,384,685,686,688,687,217,172,195,184,503,218,501,173,196,185,171,502,216,197,183,213,175,506,198,187,214,176,504,199,188,215,174,505,200,186,178,208,498,201,190,179,209,499,202,191,203,177,207,500,189,181,211,497,204,193,182,212,495,205,194,180,210,496,206,192,701,702,704,703,83,68,623,608,342,81,343,66,621,606,67,344,82,622,607,79,71,341,619,611,80,69,339,620,609,78,70,340,618,610,63,74,348,614,603,64,72,349,612,604,613,65,73,350,605,62,77,347,617,602,60,75,345,615,600,61,76,346,616,601,670,669,672,671,226,57,20,5,513,227,514,58,18,3,51,515,225,19,4,229,53,516,16,8,230,54,517,17,6,228,52,518,15,7,50,224,511,11,1,48,222,512,9,0,10,49,223,510,2,46,220,507,14,56,47,221,508,12,59,45,219,509,13,55,680,677,679,678,532,544,520,555,231,533,232,545,521,556,543,233,531,519,557,535,547,234,523,558,536,548,235,524,559,534,546,236,522,560,550,538,237,526,561,551,539,238,527,562,525,549,537,239,563,553,541,240,529,564,554,542,241,530,565,552,540,242,528,566,689,690,691,692,313,320,291,587,120,314,121,318,292,585,319,122,312,293,586,309,316,123,294,590,310,317,124,295,588,311,315,125,296,589,326,304,126,297,582,324,305,127,298,583,299,325,303,128,584,322,307,129,300,581,323,308,130,301,579,321,306,131,302,580,697,698,700,699,99,108,647,632,91,100,92,109,645,630,110,90,101,646,631,98,111,94,643,635,96,112,95,644,633,97,113,93,642,634,114,105,89,638,627,115,106,87,636,628,637,116,107,88,629,117,104,85,641,626,118,102,86,639,624,119,103,84,640,625,661,662,664,663,437,400,424,412,27,435,28,401,425,413,399,29,436,423,411,440,403,30,427,415,438,404,31,428,416,439,402,32,426,414,406,443,25,430,418,407,441,26,431,419,429,405,442,24,417,409,446,21,433,421,410,444,22,434,422,408,445,23,432,420,682,681,684,683,135,141,596,158,335,136,333,142,594,156,143,334,137,595,157,134,144,338,599,154,132,145,336,597,155,133,146,337,598,153,652,653,330,655,654,656,657,331,659,658,650,649,648,332,651,147,140,329,593,152,148,138,327,591,150,149,139,328,592,151,693,694,696,695,269,279,257,245,569,267,567,280,255,243,281,568,268,256,244,272,282,572,260,248,270,283,570,258,246,271,284,571,259,247,285,275,575,263,251,286,273,573,261,249,262,287,274,574,250,288,278,578,266,254,289,276,576,264,252,290,277,577,265,253,666,665,668,667,474,484,469,453,167,475,165,485,470,454,483,166,476,468,455,473,487,170,465,456,471,488,168,466,457,472,486,169,467,458,490,480,162,460,451,491,481,163,461,452,459,489,482,164,450,493,479,161,463,447,494,477,159,464,448,492,478,160,462,449,674,673,676,675 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#58666f8071d01f531e6f0c3147dedbb33da52b01b6615c3c73eb980e964d7179, 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 17:30:23 · history