Equation 677 Database

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Magma 0caf15565c0a…

magma 0caf15565c0a
Size
705
Isomorphism class hash
0caf15565c0a90a2ef6e27ddce0e5fc0092582c87ea56c2033a1808a4e310838
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 20:37:52
Display reorder
660,318,282,306,294,329,316,280,304,292,330,317,281,305,293,328,285,321,309,297,332,283,319,307,295,333,284,320,308,296,331,324,312,288,300,335,322,310,286,298,336,323,311,287,299,334,315,327,291,303,338,313,325,289,301,339,314,326,290,302,337,685,686,688,687,19,13,204,407,37,20,14,202,408,38,21,15,203,406,39,12,18,207,410,36,10,16,205,411,34,11,17,206,409,35,25,199,4,405,28,26,200,5,403,29,27,201,6,404,30,198,24,7,401,31,196,22,8,402,32,197,23,9,400,33,701,702,704,703,551,275,580,570,558,552,276,581,568,556,550,274,582,569,557,278,554,583,573,561,279,555,584,571,559,277,553,585,572,560,549,586,273,576,564,547,587,271,574,562,548,588,272,575,563,589,545,269,579,567,590,546,270,577,565,591,544,268,578,566,670,669,672,671,447,214,428,421,458,445,215,429,422,459,446,216,427,423,457,217,443,424,420,454,218,444,425,418,455,219,442,426,419,456,438,434,212,412,449,436,435,213,413,450,437,433,211,414,448,430,441,208,415,452,431,439,209,416,453,432,440,210,417,451,680,677,679,678,220,99,467,244,234,221,97,468,245,232,222,98,466,246,233,95,223,470,247,237,96,224,471,248,235,94,225,469,249,236,226,465,90,250,240,227,463,88,251,238,228,464,89,252,239,461,229,93,253,243,462,230,91,254,241,460,231,92,255,242,689,690,691,692,69,497,61,44,132,67,498,62,45,130,68,496,63,43,131,500,65,60,40,135,501,66,58,41,133,499,64,59,42,134,75,52,503,50,127,73,53,504,51,128,74,54,502,49,129,55,71,506,46,126,56,72,507,47,124,57,70,505,48,125,697,698,700,699,607,601,651,639,627,608,602,649,637,625,609,603,650,638,626,600,606,647,635,623,598,604,648,636,624,599,605,646,634,622,613,642,592,630,618,614,640,593,628,616,615,641,594,629,617,645,612,595,633,621,643,610,596,631,619,644,611,597,632,620,661,662,664,663,364,137,354,342,378,365,138,352,340,376,366,136,353,341,377,140,367,357,345,381,141,368,355,343,379,139,369,356,344,380,370,360,143,348,384,371,358,144,346,382,372,359,142,347,383,363,373,146,351,387,361,374,147,349,385,362,375,145,350,386,682,681,684,683,511,84,534,529,519,512,82,535,530,517,513,83,536,528,518,87,510,537,532,522,85,508,538,533,520,86,509,539,531,521,657,659,79,658,656,527,540,80,1,523,652,654,81,653,655,541,516,78,2,526,542,514,76,3,524,543,515,77,0,525,693,694,696,695,484,265,479,115,108,485,266,480,116,106,486,267,478,117,107,264,487,482,114,111,262,488,483,112,109,263,489,481,113,110,490,477,256,121,103,491,475,257,122,104,492,476,258,123,105,473,493,259,120,102,474,494,260,118,100,472,495,261,119,101,666,665,668,667,148,394,185,172,160,149,395,186,173,161,150,396,184,174,162,397,151,188,175,163,398,152,189,176,164,399,153,187,177,165,154,191,392,178,166,155,192,393,179,167,156,190,391,180,168,194,157,388,181,169,195,158,389,182,170,193,159,390,183,171,674,673,676,675 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#c84e71ca0bd6781f4c1c1e66d375057eb5ddb823e6cd89140cc4ca3da0f421d2, 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 20:37:53 · history