Equation 677 Database

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Magma 1a186f6033d7…

magma 1a186f6033d7
Size
705
Isomorphism class hash
1a186f6033d73de1d8dae0b661d1a446c879049adcfec9d80b65d577f8987771
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 15:53:28
Display reorder
660,150,152,151,155,153,154,147,148,149,146,144,145,543,544,545,542,540,541,549,550,551,548,546,547,206,204,205,209,207,208,212,210,211,215,213,214,45,46,47,44,42,43,36,37,38,39,40,41,412,413,411,408,409,410,418,419,417,414,415,416,676,692,690,683,579,581,580,577,578,576,587,585,586,583,584,582,463,464,462,466,467,465,461,459,460,457,458,456,69,70,71,68,66,67,60,61,62,63,64,65,606,607,608,609,610,611,604,605,603,600,601,602,592,593,591,588,589,590,598,599,597,594,595,596,688,693,701,697,396,398,397,401,399,400,404,402,403,407,405,406,97,98,96,100,101,99,103,104,102,106,107,105,128,126,127,131,129,130,123,124,125,122,120,121,140,138,139,143,141,142,135,136,137,134,132,133,534,535,536,537,538,539,532,533,531,528,529,530,665,668,678,671,618,620,619,623,621,622,615,616,617,614,612,613,12,13,14,15,16,17,18,19,20,21,22,23,254,252,253,257,255,256,260,258,259,263,261,262,368,366,367,371,369,370,363,364,365,362,360,361,477,478,479,476,474,475,468,469,470,471,472,473,674,681,689,684,489,491,490,487,488,486,482,480,481,485,483,484,4,5,3,1,0,2,10,11,9,6,7,8,374,372,373,377,375,376,380,378,379,383,381,382,269,267,268,265,266,264,275,273,274,271,272,270,628,629,627,624,625,626,634,635,633,630,631,632,687,700,704,698,295,294,296,297,298,299,292,293,291,288,289,290,510,511,512,513,514,515,508,509,507,504,505,506,58,59,57,54,55,56,49,50,48,52,53,51,28,29,27,24,25,26,34,35,33,30,31,32,656,654,655,659,657,658,651,652,653,650,648,649,686,695,703,699,319,318,320,321,322,323,316,317,315,312,313,314,343,344,342,346,347,345,341,339,340,337,338,336,331,332,330,334,335,333,329,327,328,325,326,324,177,178,179,176,174,175,168,169,170,171,172,173,352,353,351,348,349,350,358,359,357,354,355,356,661,662,667,666,184,183,185,182,180,181,189,190,191,188,186,187,162,163,164,165,166,167,160,161,159,156,157,158,423,424,425,422,420,421,429,430,431,428,426,427,216,217,218,219,220,221,222,223,224,225,226,227,554,552,553,557,555,556,560,558,559,563,561,562,675,680,691,682,304,303,305,302,300,301,309,310,311,308,306,307,521,519,520,517,518,516,527,525,526,523,524,522,387,388,389,386,384,385,393,394,395,392,390,391,247,248,246,250,251,249,245,243,244,241,242,240,113,111,112,109,110,108,119,117,118,115,116,114,685,694,702,696,236,235,234,238,239,237,233,231,232,229,230,228,192,193,194,195,196,197,198,199,200,201,202,203,280,281,279,276,277,278,286,287,285,282,283,284,636,637,638,639,640,641,642,643,644,645,646,647,498,499,500,501,502,503,496,497,495,492,493,494,663,669,679,670,76,75,77,74,72,73,81,82,83,80,78,79,93,94,95,92,90,91,84,85,86,87,88,89,564,565,566,567,568,569,570,571,572,573,574,575,445,446,444,448,449,447,451,452,450,454,455,453,434,432,433,437,435,436,440,438,439,443,441,442,664,672,677,673 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {64} 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 15:53:29 · history