Equation 677 Database

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Magma 956796b80466…

magma 956796b80466
Size
705
Isomorphism class hash
956796b80466bb9b9da29bacc9d39d7c5f9c62416820fc357b9a6df67000662d
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 16:36:27
Display reorder
660,587,4,46,6,597,588,5,7,47,595,8,3,586,48,596,1,590,9,45,593,0,591,10,43,594,2,589,11,44,592,54,585,53,12,603,58,583,56,13,601,51,584,59,14,602,57,581,50,15,599,52,582,49,16,600,55,580,42,17,598,687,688,686,685,403,434,392,272,421,404,435,273,393,422,271,433,405,391,423,430,402,268,388,420,431,400,269,389,418,432,401,270,390,419,425,409,398,278,412,426,410,399,279,413,424,411,397,277,414,428,408,394,274,415,429,406,395,275,416,427,407,396,276,417,703,704,701,702,558,535,554,163,568,556,536,161,555,569,162,537,557,553,570,534,561,159,550,571,532,559,160,551,572,533,560,158,552,573,541,564,545,154,574,542,562,546,152,575,543,563,544,153,576,540,567,548,157,577,538,565,549,155,578,539,566,547,156,579,671,672,670,669,131,286,74,93,442,132,287,91,72,443,92,288,130,73,444,289,134,89,77,445,290,135,90,75,446,291,133,88,76,447,284,129,80,99,440,285,127,78,97,441,283,128,79,98,439,280,125,83,95,436,281,126,81,96,437,282,124,82,94,438,679,680,678,677,292,327,332,450,313,293,325,448,333,314,449,326,294,331,315,323,295,453,328,312,324,296,451,329,310,322,297,452,330,311,318,298,338,456,304,316,299,339,454,305,317,300,337,455,306,321,301,334,459,307,319,302,335,457,308,320,303,336,458,309,692,691,690,689,493,518,481,361,505,494,519,362,482,506,363,517,495,483,507,514,492,360,480,504,515,490,358,478,502,516,491,359,479,503,509,484,472,352,496,510,485,473,353,497,508,486,474,354,498,512,487,475,355,499,513,488,476,356,500,511,489,477,357,501,699,700,698,697,202,178,190,172,212,200,176,170,188,213,171,177,201,189,214,181,205,175,193,215,179,203,173,191,216,180,204,174,192,217,184,208,196,167,218,182,206,194,168,219,183,207,195,169,220,187,211,199,166,221,185,209,197,164,222,186,210,198,165,223,663,664,662,661,642,616,638,366,614,640,617,364,639,615,365,618,641,637,613,619,645,369,634,610,620,643,367,635,611,621,644,368,636,612,622,648,629,372,605,623,646,630,370,606,624,647,628,371,604,625,651,632,375,608,626,649,633,373,609,627,650,631,374,607,682,683,684,681,237,231,84,522,144,235,232,520,85,145,521,230,236,86,143,233,234,525,87,142,652,654,523,653,655,658,659,524,657,656,229,243,146,528,137,227,241,147,526,138,228,242,148,527,136,225,239,149,531,140,226,240,150,529,141,224,238,151,530,139,695,696,693,694,66,119,467,347,39,67,120,348,468,40,346,118,68,466,41,122,69,350,470,38,123,70,351,471,36,121,71,349,469,37,117,64,465,345,30,115,65,463,343,31,116,63,464,344,32,113,60,461,341,33,114,61,462,342,34,112,62,460,340,35,667,668,665,666,384,260,27,104,248,382,261,105,28,249,103,259,383,29,247,256,387,100,26,244,257,385,101,24,245,258,386,102,25,246,266,379,18,110,254,267,380,19,111,255,265,381,20,109,253,262,378,21,106,250,263,376,22,107,251,264,377,23,108,252,675,676,673,674 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#368900d303714df43b3718b8680935166fd1150994cfe143b7c0fba0a5b985be, 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 16:36:29 · history