Equation 677 Database

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Magma 763d16f54b42…

magma 763d16f54b42
Size
705
Isomorphism class hash
763d16f54b4297a22a406b50a0a392a55fab8a5211797e15aee5f2e6ec10ce1a
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 15:51:11
Display reorder
660,654,656,655,659,657,658,651,652,653,650,648,649,142,143,141,138,139,140,133,134,132,136,137,135,281,279,280,277,278,276,287,285,286,283,284,282,38,36,37,41,39,40,44,42,43,47,45,46,80,78,79,83,81,82,75,76,77,74,72,73,669,692,689,681,382,381,383,380,378,379,372,373,374,375,376,377,355,356,354,358,359,357,353,351,352,349,350,348,394,395,393,390,391,392,385,386,384,388,389,387,61,62,60,64,65,63,67,68,66,70,71,69,365,363,364,361,362,360,371,369,370,367,368,366,684,704,698,695,634,633,635,632,630,631,624,625,626,627,628,629,607,608,606,610,611,609,605,603,604,601,602,600,647,645,646,643,644,642,638,636,637,641,639,640,27,28,29,26,24,25,33,34,35,32,30,31,617,615,616,613,614,612,623,621,622,619,620,618,666,674,673,679,432,434,433,437,435,436,440,438,439,443,441,442,410,408,409,413,411,412,416,414,415,419,417,418,397,398,396,400,401,399,403,404,402,406,407,405,273,274,275,272,270,271,264,265,266,267,268,269,422,420,421,425,423,424,428,426,427,431,429,430,670,690,687,685,485,484,483,480,481,482,490,491,489,486,487,488,466,467,465,462,463,464,457,458,456,460,461,459,454,455,453,450,451,452,445,446,444,448,449,447,100,101,99,96,97,98,106,107,105,102,103,104,479,477,478,475,476,474,470,468,469,473,471,472,686,703,697,700,514,513,515,512,510,511,504,505,506,507,508,509,537,538,539,536,534,535,528,529,530,531,532,533,527,525,526,523,524,522,518,516,517,521,519,520,91,92,90,94,95,93,89,87,88,85,86,84,551,549,550,547,548,546,542,540,541,545,543,544,682,702,696,693,226,225,227,224,222,223,216,217,218,219,220,221,250,251,249,246,247,248,241,242,240,244,245,243,237,238,239,236,234,235,228,229,230,231,232,233,211,212,210,214,215,213,209,207,208,205,206,204,263,261,262,259,260,258,254,252,253,257,255,256,661,662,663,667,310,309,311,308,306,307,300,301,302,303,304,305,335,333,334,331,332,330,326,324,325,329,327,328,322,323,321,318,319,320,313,314,312,316,317,315,155,153,154,151,152,150,146,144,145,149,147,148,293,291,292,289,290,288,299,297,298,295,296,294,668,691,688,680,557,556,555,552,553,554,562,563,561,558,559,560,583,584,582,586,587,585,581,579,580,577,578,576,571,572,570,574,575,573,569,567,568,565,566,564,19,20,18,22,23,21,17,15,16,13,14,12,593,591,592,589,590,588,599,597,598,595,596,594,683,701,699,694,7,6,8,9,10,11,4,5,3,1,0,2,120,121,122,123,124,125,126,127,128,129,130,131,108,109,110,111,112,113,114,115,116,117,118,119,496,497,495,492,493,494,502,503,501,498,499,500,57,58,59,56,54,55,48,49,50,51,52,53,664,675,671,678,197,196,195,192,193,194,202,203,201,198,199,200,170,168,169,173,171,172,176,174,175,179,177,178,158,156,157,161,159,160,164,162,163,167,165,166,337,338,336,340,341,339,343,344,342,346,347,345,181,182,180,184,185,183,187,188,186,190,191,189,665,676,672,677 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 = {62} 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 15:51:15 · history