Equation 677 Database

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Magma 5fc494a691f7…

magma 5fc494a691f7
Size
705
Isomorphism class hash
5fc494a691f7292825ce9be7cdcad7af17e5098448ae13606b2bed660636c28b
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 19:53:08
Display reorder
660,17,499,379,30,439,15,31,500,380,440,501,32,16,381,441,13,498,378,33,438,496,14,376,34,436,12,497,377,35,437,23,505,385,28,445,21,506,386,29,446,507,22,387,27,447,504,19,384,24,444,502,20,382,25,442,503,18,383,26,443,663,668,661,664,206,511,401,278,415,207,279,512,402,416,513,277,205,400,417,202,510,404,274,414,508,203,405,275,412,204,509,403,276,413,197,517,407,269,421,198,518,408,270,422,519,196,406,268,423,516,200,410,272,420,514,201,411,273,418,515,199,409,271,419,686,690,685,687,159,295,43,559,57,160,560,296,44,58,297,561,158,42,59,162,294,46,558,56,292,163,47,556,54,161,293,45,557,55,157,301,41,565,48,155,302,39,566,49,303,156,40,567,50,300,153,37,564,51,298,154,38,562,52,299,152,36,563,53,665,669,672,667,219,463,289,90,451,217,91,464,290,452,465,92,218,291,453,215,462,288,93,450,460,216,286,94,448,214,461,287,95,449,210,469,280,88,457,208,470,281,89,458,471,209,282,87,459,468,213,283,84,456,466,211,284,85,454,467,212,285,86,455,675,681,678,676,220,174,3,535,575,221,536,175,4,576,173,537,222,5,577,223,170,2,534,574,171,224,1,532,572,225,172,0,533,573,226,165,9,541,581,227,166,10,542,582,164,228,11,543,583,168,229,8,540,580,169,230,6,538,578,167,231,7,539,579,670,666,671,662,142,391,427,587,487,140,588,392,428,488,393,589,141,429,489,145,390,426,586,486,388,143,424,584,484,144,389,425,585,485,148,397,433,593,493,146,398,434,594,494,399,147,435,595,495,396,151,432,592,492,394,149,430,590,490,395,150,431,591,491,696,698,695,694,137,120,127,571,611,138,631,630,629,628,632,633,139,635,634,136,123,126,570,608,121,134,124,568,609,135,122,125,569,610,128,648,651,649,650,129,652,655,653,654,656,130,659,657,658,645,131,647,644,646,637,132,639,636,638,641,133,643,640,642,703,701,704,702,241,97,111,176,177,242,612,98,112,613,96,615,243,113,614,240,100,110,182,180,101,238,108,183,178,239,99,109,181,179,232,103,117,622,623,233,104,118,624,625,102,234,119,627,626,106,235,116,621,620,107,236,114,616,617,105,237,115,618,619,700,699,693,697,75,547,351,375,363,76,373,548,349,361,549,374,77,350,362,74,546,347,371,359,544,72,348,372,360,73,545,346,370,358,81,553,342,366,354,82,554,340,364,352,555,83,341,365,353,552,80,345,369,357,550,78,343,367,355,551,79,344,368,356,674,682,684,680,193,475,255,599,265,194,600,476,253,266,477,601,195,254,267,192,474,251,598,264,472,190,252,596,262,191,473,250,597,263,184,481,246,605,256,185,482,244,606,257,483,186,245,607,258,480,187,249,604,259,478,188,247,602,260,479,189,248,603,261,679,683,673,677,71,332,523,317,306,69,318,333,524,304,331,316,70,525,305,67,328,522,320,309,329,68,520,321,307,66,330,521,319,308,62,338,529,323,312,60,339,530,324,310,337,61,531,322,311,334,65,528,326,315,335,63,526,327,313,336,64,527,325,314,688,689,692,691 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#b2f3cd20f8767e98b3e6e1e1383f90e37f2ce11df778eec5ffdbe92cabb78104, M = {60} 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 19:53:09 · history