Equation 677 Database

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Magma 437d49cbf03b…

magma 437d49cbf03b
Size
705
Isomorphism class hash
437d49cbf03be504064974cbbfaeadfd80e7ed072cbf0cf2af2972653afe0759
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 17:31:56
Display reorder
660,470,473,460,69,468,430,433,428,70,426,453,457,440,71,451,537,533,520,68,531,497,493,481,66,491,517,513,501,67,511,597,593,60,582,591,557,553,61,542,551,577,573,62,562,571,653,657,63,642,651,613,617,64,602,611,633,637,65,622,631,688,692,694,699,462,461,467,312,469,421,420,425,313,427,443,442,450,314,452,524,522,530,315,532,484,482,490,316,492,504,502,510,317,512,584,580,318,590,592,544,541,319,550,552,564,560,320,570,572,641,644,321,650,652,600,604,322,610,612,621,624,323,630,632,691,693,698,686,78,107,158,20,326,79,105,156,18,324,80,106,157,19,325,103,81,161,23,329,104,82,159,21,327,102,83,160,22,328,98,76,15,164,332,96,77,16,162,330,97,75,17,163,331,72,101,14,167,335,73,99,12,165,333,74,100,13,166,334,681,665,671,667,410,255,249,297,350,408,256,250,298,348,409,257,251,299,349,254,413,248,296,353,252,411,246,294,351,253,412,247,295,352,261,416,288,240,356,262,414,289,241,354,263,415,290,242,355,419,260,291,243,359,417,258,292,244,357,418,259,293,245,358,677,672,683,663,472,471,475,45,474,432,431,435,46,434,455,454,459,47,458,534,535,539,44,538,494,495,499,42,498,514,515,519,43,518,594,595,36,599,598,554,555,37,559,558,574,575,38,579,578,655,654,39,659,658,615,614,40,619,618,635,634,41,639,638,703,702,695,685,477,476,478,276,479,438,437,439,277,436,441,449,456,278,448,523,521,536,279,529,483,480,496,280,489,503,500,516,281,509,583,581,282,596,589,543,540,283,556,549,563,561,284,576,569,640,643,285,656,649,601,603,286,616,609,620,623,287,636,629,696,689,700,687,464,466,463,311,465,423,424,422,309,429,445,447,444,310,446,528,526,525,307,527,488,486,485,308,487,508,506,505,306,507,588,586,302,585,587,548,546,300,545,547,568,566,301,565,567,646,648,305,645,647,606,608,303,605,607,626,628,304,625,627,701,697,704,690,202,190,362,56,214,203,191,360,54,215,201,189,361,55,213,186,198,365,59,210,187,199,363,57,211,188,200,364,58,212,181,193,51,368,205,182,194,52,366,206,180,192,53,367,204,196,184,50,371,208,197,185,48,369,209,195,183,49,370,207,675,661,679,669,273,129,109,6,386,274,130,110,7,384,275,131,108,8,385,128,272,112,9,389,126,270,113,10,387,127,271,111,11,388,120,264,4,115,392,121,265,5,116,390,122,266,3,114,391,267,123,1,118,395,268,124,0,119,393,269,125,2,117,394,673,678,664,684,144,398,175,85,338,145,396,176,86,336,146,397,174,84,337,401,147,178,88,341,399,148,179,89,339,400,149,177,87,340,404,150,91,173,344,402,151,92,171,342,403,152,90,172,343,153,407,94,169,347,154,405,95,170,345,155,406,93,168,346,666,670,668,680,219,374,132,29,228,220,372,133,27,229,221,373,134,28,230,377,218,135,25,231,375,216,136,26,232,376,217,137,24,233,380,225,35,138,234,378,226,33,139,235,379,227,34,140,236,224,383,31,141,237,222,381,32,142,238,223,382,30,143,239,662,682,674,676 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#58758ff0293182d6dd53be73984d3e209a66569482d3b8502bf477ddaee58f10, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 17:31:57 · history