Equation 677 Database

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Magma 5cb3d952bd9a…

magma 5cb3d952bd9a
Size
705
Isomorphism class hash
5cb3d952bd9a618658e749077c7563ee10c67941abdd23d06faa2f4195aae61f
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 15:31:44
Display reorder
660,172,565,268,6,445,446,566,173,269,4,447,567,174,270,5,444,175,564,271,2,176,442,562,272,3,443,177,563,273,0,178,556,436,274,12,179,557,437,275,10,180,558,438,276,11,559,181,439,277,8,278,560,182,440,9,561,183,441,279,7,668,664,671,665,316,226,303,457,16,17,227,317,301,458,18,228,318,302,459,15,319,229,299,456,320,13,230,300,454,14,321,231,298,455,322,224,22,294,448,323,225,23,292,449,324,223,24,293,450,220,325,21,297,451,295,221,326,19,452,222,327,20,296,453,687,690,686,685,130,635,138,577,611,612,636,131,136,578,613,637,132,137,579,610,133,634,141,576,134,608,632,139,574,609,135,633,140,575,128,626,602,144,568,129,627,603,142,569,127,628,604,143,570,629,124,605,147,571,145,630,125,606,572,631,126,607,146,573,672,670,669,662,307,541,339,25,469,470,542,308,337,26,471,543,309,338,27,468,306,540,335,28,304,466,538,336,29,467,305,539,334,30,313,532,460,330,31,314,533,461,328,32,315,534,462,329,33,535,312,463,333,34,331,536,310,464,35,537,311,465,332,36,678,675,684,682,41,433,505,341,421,422,434,42,506,342,423,435,40,507,340,420,37,432,504,344,38,418,430,502,345,419,39,431,503,343,47,424,412,496,347,48,425,413,497,348,46,426,414,498,346,427,43,415,499,350,500,428,44,416,351,429,45,417,501,349,663,661,667,666,193,289,409,493,479,480,290,194,410,494,478,291,195,411,495,482,192,288,408,492,190,483,286,406,490,481,191,287,407,491,184,280,477,400,484,185,281,475,401,485,186,282,476,402,486,283,187,473,403,487,404,284,188,474,488,285,189,472,405,489,694,695,697,696,112,589,647,95,114,654,655,113,652,653,656,657,111,658,659,117,108,588,644,94,109,115,586,645,92,116,110,587,646,93,103,580,120,639,101,104,581,118,640,99,102,582,119,638,100,583,106,123,642,97,643,584,107,121,98,585,105,122,641,96,701,703,704,702,355,240,203,1,79,648,238,356,204,649,650,239,357,202,651,80,354,243,206,83,352,81,241,207,84,82,353,242,205,85,361,235,77,201,86,362,236,78,199,87,363,237,76,200,88,234,360,73,197,89,198,232,358,74,90,233,359,75,196,91,698,699,700,693,162,623,62,267,553,554,624,160,63,265,555,625,161,61,266,552,165,622,65,263,163,550,620,66,264,551,164,621,64,262,168,614,544,68,258,166,615,545,69,256,167,616,546,67,257,617,171,547,71,261,72,618,169,548,259,619,170,549,70,260,683,679,676,677,219,374,381,599,397,398,375,217,379,600,399,373,218,380,601,396,215,370,377,598,216,394,371,378,596,395,214,372,376,597,210,365,388,387,590,208,366,389,385,591,209,364,390,386,592,368,213,391,383,593,384,369,211,392,594,367,212,393,382,595,673,674,681,680,57,252,517,158,529,530,250,55,518,159,531,251,56,519,157,528,60,255,516,154,58,526,253,514,155,527,59,254,515,156,52,247,520,508,149,53,248,521,509,150,54,249,522,510,148,246,51,523,511,152,512,244,49,524,153,245,50,525,513,151,689,692,691,688 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#1d08ed48a203bbb312f14b36e229a5f315d68c29c0949a9ef7235ea8d2bd9766, 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 15:31:49 · history