Equation 677 Database

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Magma 386142e6fd67…

magma 386142e6fd67
Size
705
Isomorphism class hash
386142e6fd6784f8d7255b8a757c2c5869f8fe3c37c806b0a77b0690601d86e0
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 16:43:26
Display reorder
660,613,619,335,628,593,620,614,333,629,594,621,615,334,630,592,338,612,618,631,596,610,336,616,632,597,617,337,633,611,595,625,341,634,604,599,339,626,635,605,600,340,627,636,606,598,624,344,637,607,602,622,342,638,608,603,623,343,639,609,601,687,688,686,685,151,65,48,400,91,63,152,49,401,92,64,150,50,399,90,51,154,61,403,94,155,52,62,404,95,60,53,402,153,93,71,54,398,149,89,55,69,396,147,87,56,70,397,148,88,67,57,394,145,85,68,58,395,146,86,66,59,393,144,84,703,704,701,702,185,10,12,328,588,6,183,14,329,586,8,184,17,327,587,18,188,3,331,591,186,20,5,332,589,1,23,330,187,590,22,9,326,180,583,11,19,324,181,584,7,21,325,182,585,15,0,322,179,582,16,2,323,177,580,13,4,321,178,581,671,672,670,669,406,428,81,438,444,426,407,82,439,445,427,405,75,440,446,77,409,424,437,443,410,78,425,435,441,423,76,436,408,442,419,74,429,412,450,72,417,430,413,451,73,418,431,411,452,422,79,432,415,449,420,80,433,416,447,421,83,434,414,448,679,680,678,677,264,460,35,469,256,461,265,33,470,257,459,266,34,468,255,31,263,463,465,259,261,32,464,466,260,462,30,467,262,258,458,26,475,270,254,24,456,476,271,252,25,457,474,272,253,454,29,471,269,250,455,27,472,267,251,453,28,473,268,249,692,691,690,689,504,515,298,535,538,513,505,299,536,539,514,506,297,534,537,301,503,518,531,541,501,302,516,532,542,517,300,533,502,540,521,304,526,510,544,305,519,527,511,545,303,520,525,512,543,524,307,529,509,547,522,308,530,507,548,523,306,528,508,546,699,700,698,697,211,213,237,229,191,214,212,238,230,189,215,210,239,228,190,240,207,216,225,194,208,241,217,226,192,218,242,227,209,193,219,243,235,202,197,244,220,236,203,195,245,221,234,201,196,222,246,231,205,200,223,247,232,206,198,224,248,233,204,199,663,664,662,661,360,371,642,167,352,369,361,640,165,353,370,362,641,166,351,645,359,374,163,355,357,643,372,164,356,373,644,162,358,354,377,648,158,366,350,646,375,156,367,348,647,376,157,368,349,380,651,161,365,346,378,649,159,363,347,379,650,160,364,345,682,683,684,681,169,561,310,571,557,562,170,311,572,558,563,168,309,570,556,313,559,560,573,555,652,314,653,654,655,658,312,659,657,656,567,316,575,172,550,317,568,576,173,551,315,569,574,171,549,566,319,578,175,553,564,320,579,176,554,565,318,577,174,552,695,696,693,694,484,494,44,276,285,492,485,42,277,286,493,483,43,278,287,47,487,490,275,288,488,45,491,273,289,489,46,274,486,290,500,39,282,482,291,40,498,283,480,292,41,499,284,481,293,496,38,281,478,294,497,36,279,479,295,495,37,280,477,296,667,668,665,666,100,110,387,130,134,108,101,388,131,132,109,99,389,129,133,390,96,113,126,137,97,391,111,127,135,112,392,128,98,136,116,385,121,106,140,386,114,122,107,138,384,115,120,105,139,119,381,124,102,143,117,382,125,103,141,118,383,123,104,142,675,676,673,674 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#3c7860e7d36dbffc79bc7c2d0a8ff0a692ab326401712ae14ddffd4858b8cd98, 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 16:43:27 · history