Equation 677 Database

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Magma 423b445ed080…

magma 423b445ed080
Size
705
Isomorphism class hash
423b445ed0802cc6472c36449265412c6c400ec0f049b83a0049fe95b0d1b363
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 19:21:02
Display reorder
704,106,94,82,70,107,71,95,83,105,69,93,81,102,90,66,78,103,91,67,79,104,92,68,80,85,73,97,61,86,74,98,62,84,72,96,60,76,88,100,64,89,77,101,65,87,75,99,63,112,113,111,108,109,110,118,119,116,114,115,117,683,680,682,681,25,543,529,39,26,40,544,530,24,41,545,528,28,542,38,532,29,540,36,533,27,541,37,531,549,535,31,45,550,536,32,46,551,534,30,47,538,548,34,44,546,539,35,42,547,537,33,43,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,224,206,246,456,222,457,204,247,223,458,205,248,227,209,459,249,225,207,460,250,226,208,461,251,212,244,219,462,210,245,220,463,211,243,221,464,240,215,218,465,213,241,216,466,214,242,217,467,237,238,239,236,234,235,228,229,233,231,232,230,669,671,668,670,402,390,378,186,403,187,391,379,404,188,392,380,405,393,189,381,406,394,190,382,407,395,191,383,388,376,400,184,389,377,401,185,387,375,399,183,372,384,396,180,385,373,397,181,386,374,398,182,361,362,360,364,365,363,367,368,369,370,371,366,679,676,678,677,487,527,514,168,488,169,525,515,486,170,526,513,490,523,171,510,491,524,172,511,489,522,173,512,518,505,485,174,516,506,483,175,517,504,484,176,508,521,481,177,519,509,482,178,520,507,480,179,497,495,496,493,494,492,503,501,498,499,500,502,689,690,688,691,638,629,615,252,636,253,627,616,637,254,628,617,641,625,255,614,639,626,256,612,640,624,257,613,635,621,644,258,633,622,642,259,634,623,643,260,620,631,647,261,632,618,645,262,630,619,646,263,606,607,608,609,610,611,604,605,602,600,601,603,692,694,693,695,125,160,145,470,123,468,161,146,124,469,159,144,121,156,473,148,122,157,471,149,120,158,472,147,166,151,131,476,167,152,129,474,165,150,130,475,154,162,127,479,163,155,128,477,164,153,126,478,142,143,141,138,139,140,133,134,135,136,137,132,661,662,660,663,283,270,311,22,284,23,271,309,282,21,272,310,286,273,18,307,287,274,19,308,285,275,20,306,268,302,281,13,269,300,279,14,267,301,280,12,305,264,277,16,265,303,278,17,266,304,276,15,293,291,292,289,290,288,299,297,294,295,296,298,685,686,684,687,335,321,348,53,333,51,322,349,334,52,323,350,331,320,49,351,332,318,50,352,330,319,48,353,312,354,326,59,313,355,324,57,314,356,325,58,357,315,329,55,316,358,327,56,317,359,328,54,336,337,338,339,340,341,342,343,347,345,346,344,698,697,699,696,439,431,417,198,440,199,429,418,438,200,430,419,442,427,201,416,443,428,202,414,441,426,203,415,422,408,437,196,420,409,435,197,421,410,436,195,411,425,433,192,423,412,434,193,424,413,432,194,447,448,449,446,444,445,453,454,451,452,450,455,666,665,667,664,585,573,561,2,586,1,574,562,587,0,575,563,584,572,5,560,582,570,3,558,583,571,4,559,564,552,576,8,565,553,577,6,566,554,578,7,555,567,579,11,568,556,580,9,569,557,581,10,593,591,592,589,590,588,599,597,594,595,596,598,674,673,675,672 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#a08efb2611f2171bf6f734a20baed2f33f3141d650739b05e30e32bcbe11c9bc, 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 19:21:03 · history