Equation 677 Database

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Magma f34bb929b82b…

magma f34bb929b82b
Size
705
Isomorphism class hash
f34bb929b82be0f36a51e9a9f740b0b5a7e6b42218e75c8fb2b93272688659dd
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 21:50:28
Display reorder
660,478,477,479,476,474,475,468,469,470,471,472,473,466,467,465,462,463,464,457,458,456,460,461,459,50,48,49,53,51,52,56,54,55,59,57,58,454,455,453,450,451,452,445,446,444,448,449,447,491,489,490,487,488,486,482,480,481,485,483,484,680,694,699,703,438,440,439,443,441,442,435,436,437,434,432,433,429,430,431,428,426,427,420,421,422,423,424,425,38,36,37,41,39,40,44,42,43,47,45,46,418,419,417,414,415,416,409,410,408,412,413,411,406,407,405,402,403,404,397,398,396,400,401,399,681,692,698,704,562,561,563,560,558,559,552,553,554,555,556,557,593,591,592,589,590,588,599,597,598,595,596,594,501,502,503,500,498,499,492,493,494,495,496,497,576,577,578,579,580,581,582,583,584,585,586,587,575,573,574,571,572,570,566,564,565,569,567,568,662,670,683,676,526,525,527,524,522,523,516,517,518,519,520,521,506,504,505,509,507,508,512,510,511,515,513,514,62,60,61,65,63,64,68,66,67,71,69,70,540,541,542,543,544,545,546,547,548,549,550,551,539,537,538,535,536,534,530,528,529,533,531,532,661,674,685,675,317,316,315,312,313,314,322,323,321,318,319,320,307,308,306,310,311,309,305,303,304,301,302,300,12,13,14,15,16,17,18,19,20,21,22,23,337,338,336,340,341,339,343,344,342,346,347,345,328,329,327,324,325,326,334,335,333,330,331,332,678,690,695,701,376,375,377,374,372,373,381,382,383,380,378,379,367,368,366,370,371,369,365,363,364,361,362,360,4,5,3,1,0,2,10,11,9,6,7,8,355,356,354,358,359,357,353,351,352,349,350,348,392,390,391,395,393,394,387,388,389,386,384,385,679,691,697,702,259,258,260,261,262,263,256,257,255,252,253,254,246,247,248,249,250,251,244,245,243,240,241,242,288,289,290,291,292,293,294,295,296,297,298,299,233,231,232,229,230,228,239,237,238,235,236,234,265,266,264,268,269,267,271,272,270,274,275,273,682,693,696,700,100,99,101,98,96,97,105,106,107,104,102,103,84,85,86,87,88,89,90,91,92,93,94,95,280,281,279,276,277,278,286,287,285,282,283,284,220,221,219,216,217,218,226,227,225,222,223,224,114,115,116,117,118,119,112,113,111,108,109,110,663,667,686,672,208,207,209,206,204,205,213,214,215,212,210,211,199,200,198,202,203,201,197,195,196,193,194,192,73,74,72,76,77,75,79,80,78,82,83,81,185,183,184,181,182,180,191,189,190,187,188,186,173,171,172,169,170,168,179,177,178,175,176,174,665,669,689,677,126,128,127,131,129,130,123,124,125,122,120,121,163,164,162,166,167,165,161,159,160,157,158,156,35,33,34,31,32,30,26,24,25,29,27,28,151,152,150,154,155,153,149,147,148,145,146,144,135,136,137,134,132,133,141,142,143,140,138,139,666,671,688,687,608,607,606,610,611,609,605,603,604,601,602,600,644,642,643,647,645,646,639,640,641,638,636,637,651,652,653,650,648,649,657,658,659,656,654,655,626,624,625,629,627,628,632,630,631,635,633,634,621,622,623,620,618,619,612,613,614,615,616,617,664,668,684,673 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {64} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:50:29 · history