Equation 677 Database

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Magma bdd7b7cc0801…

magma bdd7b7cc0801
Size
705
Isomorphism class hash
bdd7b7cc0801bf774a9e2a35f797f01d606aa5e3c1a478ee8b4c433d896281cb
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 21:49:24
Display reorder
663,219,221,220,217,218,216,227,225,226,223,224,222,388,389,387,384,385,386,394,395,393,390,391,392,136,137,135,132,133,134,142,143,141,138,139,140,312,313,314,315,316,317,318,319,320,321,322,323,157,158,156,160,161,159,163,164,162,166,167,165,660,673,675,670,611,610,609,606,607,608,601,602,600,604,605,603,127,128,126,130,131,129,125,123,124,121,122,120,532,533,531,528,529,530,538,539,537,534,535,536,471,472,473,470,468,469,477,478,479,476,474,475,113,111,112,109,110,108,119,117,118,115,116,114,683,688,687,689,105,107,106,103,104,102,98,96,97,101,99,100,342,343,344,345,346,347,340,341,339,336,337,338,408,409,410,411,412,413,414,415,416,417,418,419,356,354,355,359,357,358,351,352,353,350,348,349,240,241,242,243,244,245,246,247,248,249,250,251,662,672,674,671,619,618,620,621,622,623,616,617,615,612,613,614,558,559,560,561,562,563,556,557,555,552,553,554,490,491,489,486,487,488,481,482,480,484,485,483,4,5,3,1,0,2,10,11,9,6,7,8,544,545,543,540,541,542,550,551,549,546,547,548,665,677,680,681,575,574,573,570,571,572,565,566,564,568,569,567,625,626,624,628,629,627,631,632,630,634,635,633,93,94,95,92,90,91,84,85,86,87,88,89,496,497,495,492,493,494,502,503,501,498,499,500,253,254,252,256,257,255,259,260,258,262,263,261,661,666,667,668,403,402,404,405,406,407,400,401,399,396,397,398,331,332,330,334,335,333,329,327,328,325,326,324,236,234,235,239,237,238,231,232,233,230,228,229,17,15,16,13,14,12,23,21,22,19,20,18,29,27,28,25,26,24,35,33,34,31,32,30,691,700,701,699,278,277,276,280,281,279,283,284,282,286,287,285,311,309,310,307,308,306,302,300,301,305,303,304,295,296,294,298,299,297,293,291,292,289,290,288,43,44,42,46,47,45,41,39,40,37,38,36,273,274,275,272,270,271,264,265,266,267,268,269,698,703,704,702,69,71,70,67,68,66,62,60,61,65,63,64,511,512,510,514,515,513,509,507,508,505,506,504,583,584,582,586,587,585,581,579,580,577,578,576,645,646,647,644,642,643,636,637,638,639,640,641,172,173,171,168,169,170,178,179,177,174,175,176,690,695,696,697,375,377,376,373,374,372,383,381,382,379,380,378,196,197,195,192,193,194,202,203,201,198,199,200,145,146,144,148,149,147,151,152,150,154,155,153,206,204,205,209,207,208,212,210,211,215,213,214,438,439,440,441,442,443,436,437,435,432,433,434,669,685,686,684,595,594,596,597,598,599,592,593,591,588,589,590,516,517,518,519,520,521,522,523,524,525,526,527,457,458,456,460,461,459,463,464,462,466,467,465,455,453,454,451,452,450,446,444,445,449,447,448,648,649,650,651,652,653,654,655,656,657,658,659,664,676,678,682,49,48,50,51,52,53,54,55,56,57,58,59,366,367,368,369,370,371,364,365,363,360,361,362,422,420,421,425,423,424,428,426,427,431,429,430,187,188,186,190,191,189,185,183,184,181,182,180,73,74,72,76,77,75,79,80,78,82,83,81,679,693,694,692 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 = {62} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 21:49:25 · history