Equation 677 Database

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Magma 21f4a7fe3acb…

magma 21f4a7fe3acb
Size
705
Isomorphism class hash
21f4a7fe3acbb2effbbee86673bd08fbe14967a699be40e22580efaee9700c62
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 21:18:51
Display reorder
660,434,408,297,393,417,432,295,394,418,409,433,410,296,395,419,396,300,430,407,420,298,431,405,397,421,299,429,406,398,422,303,414,440,399,423,301,415,438,400,424,302,416,439,401,425,413,306,436,402,426,411,304,437,403,427,412,305,435,404,428,685,686,688,687,53,27,510,205,42,54,511,206,40,25,52,26,512,207,41,208,509,49,30,38,507,50,28,209,39,508,51,29,210,37,501,22,44,203,33,502,23,45,204,31,503,24,43,202,32,21,504,47,199,36,19,505,48,200,34,20,506,46,201,35,701,702,704,703,151,384,615,375,142,152,613,376,143,385,153,386,614,377,144,378,611,154,383,141,612,155,381,379,139,610,156,382,380,140,606,390,157,373,148,604,391,158,374,149,605,392,159,372,150,389,609,160,369,147,387,607,161,370,145,388,608,162,371,146,670,669,672,671,223,519,11,238,215,224,12,239,216,520,225,521,10,240,214,237,7,226,522,211,8,227,523,235,212,9,228,524,236,213,17,517,229,244,221,18,518,230,245,222,16,516,231,246,220,513,13,232,243,217,514,14,233,241,218,515,15,234,242,219,680,677,679,678,181,253,526,190,112,182,527,191,113,254,183,255,525,192,114,189,529,184,256,111,530,185,257,187,109,528,186,258,188,110,532,251,179,196,103,533,252,180,197,104,531,250,178,198,105,247,535,175,195,106,248,536,176,193,107,249,534,177,194,108,689,690,691,692,344,294,126,276,593,345,124,274,591,292,343,293,125,275,592,272,122,347,290,596,123,348,291,273,594,121,346,289,271,595,117,285,350,282,588,115,283,351,280,589,116,284,349,281,590,288,120,353,278,587,286,118,354,279,585,287,119,352,277,586,697,698,700,699,100,169,639,90,624,101,637,88,622,170,102,171,638,89,623,86,635,99,172,627,636,97,173,87,625,634,98,174,85,626,630,167,91,81,619,628,168,92,79,620,629,166,93,80,621,163,633,94,84,618,164,631,95,82,616,165,632,96,83,617,661,662,664,663,318,71,61,328,449,316,62,329,447,72,317,70,63,330,448,327,64,314,67,452,65,315,68,325,450,66,313,69,326,451,59,77,309,319,444,60,78,307,320,445,58,76,308,321,446,73,55,312,322,443,74,56,310,323,441,75,57,311,324,442,682,681,684,683,360,2,130,600,365,358,131,598,363,1,359,0,132,599,364,603,129,356,5,368,127,357,3,601,366,128,355,4,602,367,136,645,644,647,646,137,6,361,597,362,138,641,640,642,643,657,135,656,659,658,648,133,649,651,650,653,134,652,655,654,693,694,696,695,575,552,264,543,562,573,262,544,563,553,574,554,263,545,561,546,260,578,551,565,261,576,549,547,566,259,577,550,548,564,270,558,581,541,568,268,559,579,542,569,269,560,580,540,567,557,266,584,537,571,555,267,582,538,572,556,265,583,539,570,666,665,668,667,498,476,342,464,488,499,340,462,486,474,500,475,341,463,487,460,338,497,472,484,339,495,473,461,485,337,496,471,459,483,333,467,489,455,479,331,465,490,453,477,332,466,491,454,478,470,336,492,458,482,468,334,493,456,480,469,335,494,457,481,674,673,676,675 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#e6ff3ea71fab369083c7c0ebcc1e5818a214c988729d733a41fa2a4b44566c90, 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 21:18:52 · history