Equation 677 Database

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Magma 4776a96310a3…

magma 4776a96310a3
Size
705
Isomorphism class hash
4776a96310a39e369b1f476f4d05371ec3e0c1ce3e73b61fc451d47986741e6d
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 21:22:25
Display reorder
660,573,23,564,570,574,593,590,21,584,594,22,550,553,544,554,633,19,624,630,634,653,20,644,650,654,613,18,604,610,614,533,524,14,530,534,493,484,12,490,494,513,504,13,510,514,442,447,17,445,448,464,473,15,470,474,424,433,16,430,434,687,694,692,686,560,119,566,565,575,580,585,117,586,595,118,545,541,546,555,621,115,626,625,635,640,116,646,645,655,601,114,606,605,615,521,526,110,525,535,480,486,108,485,495,501,506,109,505,515,452,450,113,443,449,466,460,111,465,475,426,420,112,425,435,698,696,703,704,103,149,163,222,247,104,223,147,164,248,148,224,102,162,246,106,145,166,225,250,107,146,167,226,251,105,144,165,227,249,101,161,155,220,245,99,159,153,221,243,100,160,154,219,244,157,97,151,216,241,158,98,152,217,242,156,96,150,218,240,664,661,675,662,391,29,283,355,307,392,356,27,284,308,28,354,390,282,306,394,25,286,358,310,395,26,287,359,311,393,24,285,357,309,389,281,35,353,305,387,279,33,351,303,388,280,34,352,304,277,385,31,349,301,278,386,32,350,302,276,384,30,348,300,673,669,681,666,567,11,571,569,568,587,589,9,591,588,10,549,547,551,548,627,7,631,629,628,647,8,651,649,648,607,6,611,609,608,527,531,2,529,528,487,491,1,489,488,507,511,0,509,508,446,444,5,454,453,471,467,3,469,468,431,427,4,429,428,691,693,695,689,562,82,572,577,576,582,596,83,592,597,81,557,542,552,556,622,78,632,637,636,642,79,652,656,657,602,80,612,617,616,522,532,73,536,537,482,492,74,496,497,502,512,72,516,517,455,451,76,456,457,472,461,77,477,476,432,422,75,436,437,701,702,697,690,579,87,578,561,563,599,581,88,598,583,89,540,559,558,543,639,86,638,620,623,659,84,658,641,643,619,85,618,600,603,538,539,93,520,523,498,499,94,481,483,518,519,95,500,503,459,458,92,441,440,479,478,90,463,462,439,438,91,421,423,700,699,685,688,171,208,232,343,367,172,344,209,233,368,207,342,173,231,366,170,204,228,346,370,168,205,229,347,371,169,206,230,345,369,177,238,214,341,365,178,239,215,339,363,179,237,213,340,364,234,176,210,337,361,235,174,211,338,362,236,175,212,336,360,672,677,679,682,411,38,410,259,271,413,260,36,412,272,37,258,408,409,270,416,41,417,262,274,419,39,418,263,275,414,40,415,261,273,407,406,44,257,269,402,403,42,255,267,404,405,43,256,268,399,398,47,253,265,400,401,45,254,266,397,396,46,252,264,663,665,684,683,331,50,137,130,379,332,131,48,135,380,49,129,330,136,378,334,53,133,126,382,335,51,134,127,383,333,52,132,128,381,329,143,56,121,377,327,141,54,122,375,328,142,55,120,376,139,325,59,124,373,140,326,57,125,374,138,324,58,123,372,667,680,671,676,319,65,197,190,295,320,191,63,195,296,64,189,318,196,294,322,61,193,186,298,323,62,194,187,299,321,60,192,188,297,317,203,71,181,293,315,201,69,182,291,316,202,70,180,292,199,313,67,184,289,200,314,68,185,290,198,312,66,183,288,674,668,670,678 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#ebc786cbc6f59f4fde563d64e7e77b74986c3576b2c4677bed47ecf46da1acd3, M = {60} 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 21:22:26 · history