Equation 677 Database

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Magma b260d94036d4…

magma b260d94036d4
Size
705
Isomorphism class hash
b260d94036d469437eef0cb6fc146dc3f693eddf7897bae05825ae1ff3df86b5
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 19:06:52
Display reorder
704,131,107,111,152,112,129,150,105,113,106,130,151,103,110,127,155,104,108,128,153,102,109,126,154,117,98,147,122,118,96,148,120,119,97,149,121,101,116,146,125,99,114,144,123,100,115,145,124,135,136,137,134,132,133,141,142,139,140,138,143,681,683,682,680,580,180,566,552,564,581,553,181,565,182,579,554,183,569,576,555,184,567,577,556,185,568,578,557,572,186,558,586,570,187,559,587,571,188,560,585,189,575,561,582,190,573,562,583,191,574,563,584,648,649,650,651,652,653,654,655,658,656,657,659,702,701,700,703,412,3,447,443,448,413,441,4,449,5,411,442,2,446,408,439,1,444,409,440,0,445,410,438,453,9,434,418,454,10,432,419,455,11,433,417,8,452,437,414,6,450,435,415,7,451,436,416,424,425,423,420,421,422,430,431,428,426,427,429,670,669,668,671,347,30,327,316,328,345,317,31,329,32,346,315,33,326,343,312,34,324,344,313,35,325,342,314,333,28,322,338,334,29,323,336,335,27,321,337,24,332,318,341,25,330,319,339,26,331,320,340,352,353,351,348,349,350,358,359,356,354,355,357,677,679,678,676,551,178,531,527,532,549,525,179,533,177,550,526,174,530,547,523,175,528,548,524,176,529,546,522,537,169,518,542,538,170,516,540,539,168,517,541,172,536,521,545,173,534,519,543,171,535,520,544,508,509,507,504,505,506,514,515,512,510,511,513,691,689,688,690,249,645,231,218,232,250,216,646,233,647,251,217,644,230,248,221,642,228,246,219,643,229,247,220,237,636,224,240,238,637,222,241,239,638,223,242,639,236,227,243,640,234,225,244,641,235,226,245,205,206,204,208,209,207,211,212,213,214,215,210,695,692,693,694,486,164,469,466,470,487,467,162,468,163,488,465,167,472,489,462,165,473,490,463,166,471,491,464,475,159,457,484,476,160,458,485,474,161,456,483,158,478,460,480,156,479,461,481,157,477,459,482,499,500,498,502,503,501,497,495,492,493,494,496,661,662,660,663,276,37,264,252,265,277,253,38,266,36,278,254,40,267,279,255,41,268,280,256,39,269,281,257,270,43,258,282,271,44,259,283,272,42,260,284,46,273,261,285,47,274,262,286,45,275,263,287,290,288,289,293,291,292,296,294,298,299,297,295,687,685,684,686,49,301,91,73,92,50,74,302,90,300,48,72,304,94,52,76,305,95,53,77,303,93,51,75,89,307,79,55,87,308,80,56,88,306,78,54,310,85,82,58,311,86,83,59,309,84,81,57,68,66,67,71,69,70,63,64,61,62,60,65,696,698,699,697,393,16,380,361,378,394,362,17,379,15,395,360,12,383,392,364,13,381,390,365,14,382,391,363,375,22,367,384,376,23,368,385,377,21,366,386,18,374,370,387,19,372,371,388,20,373,369,389,406,407,405,402,403,404,397,398,399,400,401,396,664,666,667,665,614,195,607,594,608,612,595,196,606,197,613,596,194,610,617,597,192,611,615,598,193,609,616,599,605,201,592,620,603,202,593,618,604,203,591,619,200,601,588,623,198,602,589,621,199,600,590,622,627,628,629,626,624,625,633,634,631,632,630,635,672,674,675,673 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#8782a898cb34e59b9ea1a81d727d55f661339e265a029f2d4530f64cefd9daa9, 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 19:06:53 · history