Equation 677 Database

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Magma e8ed6db14dba…

magma e8ed6db14dba
Size
705
Isomorphism class hash
e8ed6db14dba28ad1a4fc268a426ff888f938cc4ee2963023753c15e4424c0f5
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 20:31:53
Display reorder
704,128,147,162,178,126,148,163,179,127,149,164,177,131,146,165,174,129,144,166,175,130,145,167,176,123,153,160,169,124,154,161,170,125,155,159,168,152,122,156,172,150,120,157,173,121,151,158,171,140,138,139,143,141,142,135,136,133,134,132,137,683,681,682,680,84,280,288,28,85,281,289,29,86,279,290,27,87,276,291,24,88,277,292,25,89,278,293,26,90,286,294,34,91,287,295,35,92,285,296,33,282,93,297,30,283,94,298,31,95,284,299,32,648,649,650,651,652,653,654,655,658,656,657,659,701,702,700,703,69,631,595,603,70,632,596,604,71,630,594,605,68,634,598,602,66,635,599,600,67,633,597,601,60,629,593,609,61,627,591,610,62,628,592,611,625,63,589,608,626,64,590,606,65,624,588,607,618,619,620,621,622,623,616,617,614,612,613,615,669,670,668,671,49,536,503,506,50,534,501,504,48,535,502,505,52,539,499,509,53,537,500,507,51,538,498,508,55,531,494,512,56,532,492,510,54,533,493,511,530,58,497,515,528,59,495,513,57,529,496,514,527,525,526,523,524,522,518,516,520,521,519,517,679,677,678,676,80,235,244,253,78,236,245,254,79,234,243,252,83,238,240,256,81,239,241,257,82,237,242,255,75,233,250,259,76,231,251,260,77,232,249,258,229,74,246,262,230,72,247,263,73,228,248,261,268,269,267,264,265,266,274,275,272,270,271,273,689,691,688,690,112,353,364,374,113,351,365,372,111,352,363,373,108,349,360,377,109,350,361,375,110,348,362,376,118,359,370,380,119,357,371,378,117,358,369,379,355,114,366,383,356,115,367,381,116,354,368,382,394,395,393,390,391,392,385,386,387,388,389,384,692,695,693,694,638,226,186,203,636,227,187,201,637,225,188,202,641,222,189,199,639,223,190,200,640,224,191,198,644,217,184,194,642,218,185,192,643,216,183,193,220,647,180,197,221,645,181,195,646,219,182,196,204,205,206,207,208,209,210,211,215,213,214,212,662,661,660,663,22,406,414,431,23,407,415,429,21,405,416,430,18,402,417,427,19,403,418,428,20,404,419,426,13,397,412,422,14,398,413,420,12,396,411,421,400,16,408,425,401,17,409,423,15,399,410,424,432,433,434,435,436,437,438,439,443,441,442,440,685,687,684,686,43,489,444,467,44,490,445,465,42,491,446,466,46,488,447,463,47,486,448,464,45,487,449,462,41,480,450,458,39,481,451,456,40,482,452,457,483,37,453,461,484,38,454,459,36,485,455,460,468,469,470,471,472,473,474,475,479,477,478,476,698,696,699,697,2,548,560,572,1,546,558,570,0,547,559,571,5,551,563,575,3,549,561,573,4,550,562,574,8,543,555,567,6,544,556,568,7,545,557,569,542,11,554,566,540,9,552,564,10,541,553,565,582,583,584,585,586,587,580,581,578,576,577,579,666,664,667,665,100,340,305,317,101,341,303,315,99,339,304,316,96,336,301,313,97,337,302,314,98,338,300,312,106,346,311,323,107,347,309,321,105,345,310,322,342,102,307,319,343,103,308,320,104,344,306,318,327,328,329,326,324,325,333,334,331,332,330,335,674,672,675,673 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#bef86252e34aac6c2a18a1e8b323957fca09c4d4a3c476c0116e0c729e633257, 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 20:31:54 · history