Equation 677 Database

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Magma ecc8034a0e88…

magma ecc8034a0e88
Size
705
Isomorphism class hash
ecc8034a0e880e4bdc40abdc60c602e6ba6493d202cf7342878bade1b224b0d1
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 16:40:04
Display reorder
704,152,116,163,128,150,114,164,126,115,127,151,162,119,155,166,131,153,117,167,129,154,118,165,130,147,111,161,123,148,112,159,124,149,113,160,125,110,146,157,122,108,144,158,120,109,145,156,121,138,139,140,141,142,143,136,137,134,132,133,135,681,683,682,680,549,107,86,33,550,105,84,34,106,35,551,85,103,548,89,32,546,104,87,30,547,102,88,31,540,98,92,24,541,96,90,25,542,97,91,26,101,543,95,27,99,544,93,28,100,545,94,29,648,649,650,651,652,653,654,655,658,656,657,659,702,701,700,703,170,443,191,196,168,441,189,197,442,195,169,190,439,173,187,192,171,440,188,193,172,438,186,194,176,434,182,202,174,432,180,203,175,433,181,201,437,179,185,198,435,177,183,199,436,178,184,200,204,205,206,207,208,209,210,211,215,213,214,212,670,669,668,671,350,73,369,379,348,74,370,380,72,378,349,371,76,353,368,382,351,77,366,383,352,75,367,381,356,79,360,377,354,80,361,375,355,78,362,376,82,359,363,373,83,357,364,374,81,358,365,372,344,342,343,347,345,346,339,340,337,338,336,341,677,679,678,676,492,216,507,517,493,217,508,518,218,516,494,509,219,495,506,520,496,220,504,521,497,221,505,519,498,222,513,523,499,223,514,524,500,224,515,522,225,501,512,526,226,502,510,527,227,503,511,525,539,537,538,535,536,534,530,528,532,533,531,529,691,689,688,690,615,239,626,645,616,237,624,646,238,647,617,625,235,614,629,644,612,236,627,642,613,234,628,643,621,230,632,636,622,228,630,637,623,229,631,638,233,620,635,639,231,618,633,640,232,619,634,641,611,609,610,607,608,606,602,600,604,605,603,601,695,692,693,694,458,23,479,484,456,21,477,485,22,483,457,478,19,461,475,480,459,20,476,481,460,18,474,482,464,14,470,490,462,12,468,491,463,13,469,489,17,467,473,486,15,465,471,487,16,466,472,488,452,450,451,455,453,454,447,448,445,446,444,449,661,662,660,663,254,49,273,282,252,50,274,283,48,284,253,275,52,257,272,285,255,53,270,286,256,51,271,287,260,55,264,280,258,56,265,281,259,54,266,279,58,263,267,276,59,261,268,277,57,262,269,278,244,245,243,240,241,242,250,251,248,246,247,249,687,685,684,686,330,61,292,301,331,62,293,302,60,300,332,291,64,333,288,304,334,65,289,305,335,63,290,303,328,67,298,307,329,68,299,308,327,66,297,306,70,324,294,310,71,325,295,311,69,326,296,309,322,323,321,318,319,320,313,314,315,316,317,312,696,698,699,697,401,3,415,421,399,4,416,422,5,420,400,414,2,397,418,424,398,1,419,425,396,0,417,423,407,9,413,427,405,10,411,428,406,11,412,426,8,403,409,430,6,404,410,431,7,402,408,429,385,386,384,388,389,387,391,392,393,394,395,390,664,666,667,665,589,45,562,569,590,46,563,567,47,568,588,561,44,592,558,565,593,42,559,566,591,43,560,564,595,36,553,575,596,37,554,573,594,38,552,574,39,598,556,571,40,599,557,572,41,597,555,570,584,582,583,587,585,586,579,580,577,578,576,581,672,674,675,673 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#38a4e23a99caaa7b44b0fde217361d7389ff59fad772c7ae239f5a60818fe03a, 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 16:40:06 · history