Equation 677 Database

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Magma f3804ea5b79a…

magma f3804ea5b79a
Size
705
Isomorphism class hash
f3804ea5b79aa238f9bf1f3b60ae36eb810627287cfc07b3c4ef07740fae0d06
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 15:25:56
Display reorder
660,140,438,33,213,558,439,559,141,36,211,437,557,139,40,212,554,434,136,30,209,555,435,137,24,210,556,436,138,27,208,549,429,131,51,204,550,430,132,55,202,548,428,130,58,203,432,552,134,49,207,433,553,135,43,205,431,551,133,46,206,669,663,671,667,293,378,350,65,357,379,358,294,351,63,377,356,295,352,64,360,374,292,353,61,361,375,290,354,62,359,376,291,355,60,363,369,284,348,71,364,370,285,349,69,362,368,286,347,70,372,366,287,344,67,373,367,288,345,68,371,365,289,346,66,689,690,687,688,162,171,641,606,522,169,523,160,642,607,170,521,161,640,605,518,167,165,637,602,519,168,163,638,603,520,166,164,639,604,513,177,157,632,597,514,175,158,633,598,512,176,159,631,596,173,516,156,635,600,174,517,154,636,601,172,515,155,634,599,672,666,670,665,5,303,546,582,386,304,387,3,547,583,302,388,4,545,581,389,306,0,542,578,390,307,2,543,579,391,305,1,544,580,384,301,11,537,573,385,299,9,538,574,383,300,10,536,572,297,380,7,540,576,298,381,8,541,577,296,382,6,539,575,683,673,680,678,315,415,486,426,403,413,401,316,487,427,414,402,314,485,425,399,411,318,482,422,400,412,319,483,423,398,410,317,484,424,394,406,313,477,417,392,404,311,478,418,393,405,312,476,416,409,397,309,480,420,407,395,310,481,421,408,396,308,479,419,664,668,661,662,144,498,214,474,534,499,535,142,215,475,497,533,143,216,473,530,494,147,217,470,531,495,145,218,471,532,496,146,219,472,525,489,150,220,465,526,490,148,221,466,524,488,149,222,464,492,528,153,223,468,493,529,151,224,469,491,527,152,225,467,693,695,694,697,16,618,653,72,102,659,658,17,656,657,617,101,15,652,79,105,614,12,649,80,103,615,13,650,81,104,616,14,651,82,100,609,22,644,78,98,610,23,645,76,99,608,21,643,77,612,96,18,647,74,613,97,19,648,75,611,95,20,646,73,703,701,704,702,329,230,52,237,510,654,511,330,54,655,229,509,331,57,241,506,226,328,48,238,507,227,326,42,239,508,228,327,45,240,501,236,320,25,245,502,234,321,28,246,500,235,322,31,247,232,504,323,34,244,233,505,324,37,242,231,503,325,39,243,698,699,700,696,200,129,450,570,594,127,595,201,451,571,128,593,199,449,569,590,125,196,446,566,591,126,197,447,567,592,124,198,448,568,585,120,191,441,561,586,118,192,442,562,584,119,190,440,560,123,588,194,444,564,121,589,195,445,565,122,587,193,443,563,674,675,679,681,343,251,281,260,629,252,630,341,282,261,253,628,342,283,262,625,250,339,280,263,626,248,340,278,264,627,249,338,279,265,620,257,334,272,266,621,258,332,273,267,619,259,333,274,268,256,623,337,275,269,254,624,335,276,270,255,622,336,277,271,682,677,676,684,41,182,86,116,462,183,463,35,87,117,181,461,38,88,115,458,178,29,85,112,459,179,32,83,113,460,180,26,84,114,453,188,59,92,107,454,189,53,93,108,452,187,56,94,106,184,456,47,91,110,185,457,50,89,111,186,455,44,90,109,685,692,691,686 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#198f8683bee40b5fe0cfed42350fb71daef6a15506139cdcf5a71dcf11978025, 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 15:25:58 · history