Equation 677 Database

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Magma 132ec822d476…

magma 132ec822d476
Size
705
Isomorphism class hash
132ec822d4765d8fb473ff1dfaa33cd25296414e193ee00faf70390d9053c764
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 20:47:54
Display reorder
660,308,11,296,284,263,306,9,294,282,261,307,10,295,283,262,7,304,292,280,266,8,305,293,281,264,6,303,291,279,265,287,299,2,275,269,285,297,1,273,267,286,298,0,274,268,302,290,5,278,272,300,288,3,276,270,301,289,4,277,271,666,671,668,663,545,140,569,67,391,546,138,570,68,392,544,139,568,66,393,136,541,565,70,394,137,542,566,71,395,135,543,567,69,396,560,536,131,99,397,561,537,129,103,398,559,535,130,72,399,539,563,134,74,400,540,564,132,75,401,538,562,133,73,402,690,685,686,687,460,224,641,509,473,461,222,642,510,474,462,223,640,508,472,220,459,637,505,469,221,457,638,506,470,219,458,639,507,471,632,451,215,500,464,633,452,213,501,465,631,453,214,499,463,454,635,218,503,467,455,636,216,504,468,456,634,217,502,466,665,664,662,672,176,406,155,142,188,174,407,153,143,186,175,408,154,141,187,405,172,158,145,184,403,173,156,146,185,404,171,157,144,183,161,167,412,148,179,159,165,413,149,177,160,166,414,147,178,170,164,411,151,182,168,162,409,152,180,169,163,410,150,181,683,673,678,675,617,65,593,437,424,618,63,594,438,425,616,64,592,436,426,61,613,589,433,423,62,614,590,434,421,60,615,591,435,422,584,608,102,428,415,585,609,12,429,416,583,607,98,427,417,611,587,59,431,418,612,588,57,432,419,610,586,58,430,420,661,667,670,669,533,309,581,497,251,534,310,582,498,249,532,311,580,496,250,312,529,577,493,254,313,530,578,494,252,314,531,579,495,253,572,524,315,488,257,573,525,316,489,255,571,523,317,487,256,527,575,318,491,260,528,576,319,492,258,526,574,320,490,259,694,693,695,696,104,38,653,14,13,658,39,659,656,657,100,40,652,28,27,37,94,649,32,31,35,95,650,34,33,36,96,651,30,29,644,92,44,25,26,645,93,45,21,22,643,91,46,23,24,88,647,43,17,18,89,648,41,20,19,90,646,42,15,16,703,702,701,704,368,326,361,349,338,654,324,359,655,336,369,325,360,348,337,322,371,357,345,334,323,372,358,346,335,321,370,356,347,333,367,374,332,355,344,365,375,330,353,342,366,373,331,354,343,377,363,328,351,340,378,364,329,352,341,376,362,327,350,339,699,698,700,697,52,127,521,239,485,50,128,522,237,486,51,126,520,238,484,123,48,517,242,481,124,49,518,240,482,125,47,519,241,483,512,101,118,245,476,513,56,119,243,477,511,97,117,244,475,54,515,121,248,479,55,516,122,246,480,53,514,120,247,478,677,676,682,679,385,208,557,629,449,386,209,558,630,450,387,207,556,628,448,211,388,553,625,445,212,389,554,626,446,210,390,555,627,447,548,383,206,620,440,549,384,204,621,441,547,382,205,619,439,379,551,202,623,443,380,552,203,624,444,381,550,201,622,442,684,674,681,680,83,195,233,605,113,84,196,231,606,111,82,197,232,604,112,198,86,236,601,116,199,87,234,602,114,200,85,235,603,115,228,81,193,596,108,229,79,194,597,109,230,80,192,595,110,77,227,189,599,107,78,225,190,600,105,76,226,191,598,106,688,692,689,691 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#d5c298f3996cbe1c131ede943bdfb3db88b47e8bf729cba865448336ce4ceccf, 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 20:47:55 · history