Equation 677 Database

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Magma 3819c0e1876f…

magma 3819c0e1876f
Size
705
Isomorphism class hash
3819c0e1876f2243eb720433eb574f320462662543390df7df0b2ef2ed1e2a3f
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 15:09:57
Display reorder
660,325,348,632,359,337,633,326,357,338,349,634,350,324,358,336,321,635,347,362,333,322,636,345,360,334,323,637,346,361,335,638,354,365,331,343,639,355,363,332,344,640,356,364,330,342,353,641,368,327,339,351,642,366,328,340,329,352,643,367,341,687,688,686,685,214,244,192,461,183,193,215,459,184,245,194,243,213,460,185,217,191,247,464,186,218,189,248,462,187,216,190,246,463,188,198,242,456,220,181,199,240,457,221,182,200,241,458,219,180,238,197,455,223,177,239,195,453,224,178,222,237,196,454,179,703,704,701,702,103,128,319,627,107,320,104,628,105,126,318,127,102,626,106,99,315,124,630,110,100,316,125,631,108,101,317,123,629,109,310,119,625,94,113,311,117,623,95,111,309,118,624,93,112,122,313,621,97,116,120,314,622,98,114,96,121,312,620,115,671,672,670,669,481,502,249,471,494,250,482,472,492,503,251,501,480,473,493,477,252,505,474,490,478,253,506,475,491,479,254,504,476,489,255,508,469,487,500,256,509,470,488,498,257,507,468,486,499,511,258,465,483,496,512,259,466,484,497,485,510,260,467,495,679,680,678,677,558,528,262,539,521,263,559,537,519,529,261,530,560,538,520,557,265,527,542,524,555,266,525,540,522,556,264,526,541,523,268,534,545,549,516,269,535,543,550,517,267,536,544,551,518,533,271,548,552,515,531,272,546,553,513,554,532,270,547,514,692,691,690,689,294,589,68,600,581,69,295,601,579,590,70,588,296,602,580,293,67,585,599,584,291,65,586,597,582,292,66,587,598,583,74,595,606,285,576,75,596,607,286,577,76,594,608,287,578,591,73,605,288,575,592,71,603,289,573,290,593,72,604,574,699,700,698,697,158,135,165,145,20,166,156,146,21,136,167,137,157,144,22,154,168,138,141,19,155,169,139,142,17,153,170,140,143,18,171,133,151,164,26,172,134,152,162,27,173,132,150,163,28,129,174,147,160,25,130,175,148,161,23,159,131,176,149,24,663,664,662,661,385,406,646,377,396,644,386,375,397,407,645,405,384,376,398,381,649,409,380,395,382,647,410,378,393,383,648,408,379,394,652,412,372,391,402,650,413,373,392,403,651,411,374,390,404,415,655,371,387,401,416,653,369,388,399,389,414,654,370,400,682,683,684,681,90,616,306,84,3,307,91,85,4,617,308,615,92,83,2,89,305,619,87,1,657,303,658,656,659,88,304,618,86,0,297,614,82,12,6,298,612,80,13,7,299,613,81,11,5,610,300,78,15,9,611,301,79,16,10,14,609,302,77,8,695,696,693,694,64,32,565,281,42,566,62,279,43,33,564,34,63,280,41,60,561,31,284,45,61,562,29,282,46,59,563,30,283,44,571,38,276,55,48,572,39,277,53,49,570,40,278,54,47,37,567,275,58,51,35,568,273,56,52,57,36,569,274,50,667,668,665,666,434,231,209,423,443,207,432,424,441,232,208,233,433,425,442,430,212,234,426,446,431,210,235,427,444,429,211,236,428,445,204,229,421,440,449,205,230,422,438,447,206,228,420,439,448,225,203,417,436,452,226,201,418,437,450,435,227,202,419,451,675,676,673,674 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#06e28404eb43925716bfc8e4d73e8cc7ccb918742e903c176b52de636b48f456, 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 15:09:59 · history