Equation 677 Database

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Magma 2f625aea0074…

magma 2f625aea0074
Size
705
Isomorphism class hash
2f625aea007472c58321d558eaaa5415fe9e011cd86708c99d17f0727216f5d5
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 19:12:36
Display reorder
660,173,31,247,124,462,174,245,125,463,32,172,30,246,126,461,34,176,243,127,458,35,177,244,128,459,33,175,242,129,460,238,29,171,122,453,236,27,169,123,454,237,28,170,121,452,25,241,167,118,456,26,239,168,119,457,120,24,240,166,455,671,662,664,667,424,367,303,438,371,422,304,439,372,365,423,366,302,437,373,363,427,306,434,370,364,425,307,435,368,362,426,305,436,369,301,358,419,429,377,299,356,420,430,378,300,357,421,428,379,361,297,418,432,376,359,298,416,433,374,431,360,296,417,375,690,685,688,686,641,546,271,414,474,642,269,415,475,547,640,545,270,413,473,542,637,267,410,470,543,638,268,411,471,544,639,266,412,472,262,537,632,405,465,260,538,633,406,466,261,536,631,404,464,540,265,635,408,468,541,263,636,409,469,407,539,264,634,467,672,668,665,663,19,450,313,161,387,20,311,162,388,451,18,449,312,160,386,446,22,309,164,390,447,23,310,165,391,448,21,308,163,389,319,441,17,159,385,317,442,15,157,383,318,440,16,158,384,444,315,13,155,381,445,316,14,156,382,154,443,314,12,380,675,674,680,681,321,402,86,594,570,322,87,595,571,403,320,401,85,593,569,398,324,82,590,566,399,325,83,591,567,400,323,84,592,568,92,393,327,585,561,93,394,328,586,562,91,392,326,584,560,396,88,330,588,564,397,89,331,589,565,587,395,90,329,563,666,661,669,670,498,134,47,248,582,499,45,249,583,135,497,133,46,250,581,130,494,43,251,578,131,495,44,252,579,132,496,42,253,580,38,140,489,254,573,36,141,490,255,574,37,139,488,256,572,136,41,492,257,576,137,39,493,258,577,259,138,40,491,575,694,693,697,696,48,59,71,653,618,658,72,659,656,657,52,63,70,652,617,60,49,74,649,614,61,50,75,650,615,62,51,73,651,616,77,67,56,644,609,78,68,57,645,610,76,69,58,643,608,66,80,55,647,612,64,81,53,648,613,646,65,79,54,611,702,703,701,704,189,340,151,522,178,654,152,523,655,338,190,339,153,521,182,343,191,150,518,179,341,192,148,519,180,342,193,149,520,181,142,335,198,513,186,143,336,199,514,187,144,337,197,512,188,334,145,194,516,185,332,146,195,517,183,515,333,147,196,184,699,698,700,695,486,558,113,291,231,487,114,292,232,559,485,557,112,290,230,554,482,116,294,234,555,483,117,295,235,556,484,115,293,233,111,549,477,289,229,109,550,478,287,227,110,548,476,288,228,552,107,480,285,225,553,108,481,286,226,284,551,106,479,224,676,679,683,673,606,534,353,510,629,607,354,511,630,535,605,533,355,509,628,530,602,352,506,625,531,603,350,507,626,532,604,351,508,627,344,525,597,501,620,345,526,598,502,621,346,524,596,500,619,528,347,600,504,623,529,348,601,505,624,503,527,349,599,622,682,678,684,677,209,101,3,221,279,210,4,222,280,102,211,100,5,223,278,104,208,2,220,282,105,206,1,218,283,103,207,0,219,281,9,99,200,212,277,10,97,201,213,275,11,98,202,214,276,95,8,203,215,273,96,6,204,216,274,217,94,7,205,272,687,691,689,692 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#9017e525a3aedea68e654a603b277c6c50731afc33f3d9497441ab6abb8d2314, 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 19:12:37 · history