Equation 677 Database

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Magma d1dc92bc732f…

magma d1dc92bc732f
Size
705
Isomorphism class hash
d1dc92bc732f54d6707de0095e164316591f18d4ec681a4e4c10909a0d87ce06
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 20:08:15
Display reorder
660,385,613,394,265,275,386,614,395,266,273,612,384,393,264,274,388,616,390,268,271,389,617,391,269,272,387,615,392,267,270,619,383,400,263,281,620,381,401,261,279,618,382,399,262,280,379,622,396,259,277,380,623,397,260,278,378,621,398,258,276,687,688,686,685,44,64,229,470,2,42,65,230,468,1,63,43,228,469,0,47,60,232,473,5,45,61,233,471,3,46,62,231,472,4,70,39,227,465,8,71,40,225,466,6,69,41,226,467,7,38,66,223,464,11,36,67,224,462,9,37,68,222,463,10,703,704,701,702,14,607,348,364,368,12,608,349,365,366,606,13,350,363,367,17,610,351,360,371,15,611,352,361,369,16,609,353,362,370,605,20,346,355,374,603,18,347,356,372,604,19,345,354,373,23,601,342,358,377,21,602,343,359,375,22,600,344,357,376,671,672,670,669,498,236,49,482,497,499,234,50,480,495,235,500,48,481,496,501,239,52,485,493,502,237,53,483,494,503,238,51,484,492,242,504,55,477,488,240,505,56,478,486,241,506,54,479,487,507,245,58,476,491,508,243,59,474,489,509,244,57,475,490,679,680,678,677,164,72,518,531,251,162,73,516,532,249,74,163,517,533,250,167,75,521,530,247,165,76,519,528,248,166,77,520,529,246,78,170,513,522,257,79,168,514,523,255,80,169,515,524,256,173,81,512,525,253,171,82,510,526,254,172,83,511,527,252,692,691,690,689,312,590,328,194,92,313,588,329,192,90,589,314,327,193,91,315,593,324,197,95,316,591,325,195,93,317,592,326,196,94,585,310,319,189,87,586,311,320,190,88,587,309,318,191,89,306,584,322,188,86,307,582,323,186,84,308,583,321,187,85,699,700,698,697,120,155,136,139,26,121,153,137,140,24,154,122,135,138,25,123,151,132,142,29,124,152,133,143,27,125,150,134,141,28,161,118,127,145,32,159,119,128,146,30,160,117,126,144,31,114,157,130,148,35,115,158,131,149,33,116,156,129,147,34,663,664,662,661,200,626,410,425,292,198,624,408,423,293,625,199,409,424,291,203,629,413,421,288,201,627,411,422,289,202,628,412,420,290,632,206,405,416,283,630,204,406,414,284,631,205,407,415,282,209,635,404,419,286,207,633,402,417,287,208,634,403,418,285,682,683,684,681,649,331,651,648,650,652,332,655,653,654,330,656,659,657,658,644,334,647,645,646,636,335,638,637,639,640,333,643,641,642,337,99,597,104,111,338,100,598,102,112,336,101,599,103,113,98,340,596,107,110,96,341,594,105,108,97,339,595,106,109,695,696,693,694,537,176,556,558,573,538,174,557,559,574,175,539,555,560,575,536,179,552,561,572,534,177,553,562,570,535,178,554,563,571,182,543,547,564,579,180,544,548,565,580,181,545,546,566,581,542,185,550,567,578,540,183,551,568,576,541,184,549,569,577,667,668,665,666,297,216,434,449,452,298,217,432,447,450,218,299,433,448,451,296,219,437,445,455,294,220,435,446,453,295,221,436,444,454,214,303,429,440,458,215,304,430,438,456,213,305,431,439,457,302,210,428,443,461,300,211,426,441,459,301,212,427,442,460,675,676,673,674 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#ba8e767ab0f178377cc5ca58de8baa4e7db92c571ba3737b1b055d153a9d0c2e, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 20:08:16 · history