Equation 677 Database

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Magma 276ed048c328…

magma 276ed048c328
Size
705
Isomorphism class hash
276ed048c3282b8f3fb1673985e2671ef8a7411935dd4664c54945e91ee10724
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 21:18:16
Display reorder
660,643,644,656,257,642,603,604,255,616,602,256,624,623,636,622,564,563,253,576,562,584,583,254,596,582,544,543,252,556,542,463,464,476,263,462,424,425,434,261,423,443,444,456,262,442,523,524,536,259,522,483,484,496,260,482,503,504,516,258,502,687,688,695,700,641,651,658,21,650,601,611,22,618,610,23,631,621,638,630,571,560,20,578,570,591,580,18,598,590,551,540,19,558,550,460,471,478,12,470,421,430,436,13,429,440,451,458,14,450,520,531,538,15,530,481,491,498,16,490,500,511,518,17,510,694,702,698,704,299,97,226,79,419,297,98,80,227,417,78,96,298,225,418,100,295,82,222,415,101,296,83,223,416,99,294,81,224,414,290,103,217,77,410,288,104,218,75,408,289,102,216,76,409,293,106,220,73,413,291,107,221,74,411,292,105,219,72,412,670,680,663,669,148,347,63,9,407,149,345,10,64,405,11,346,147,65,406,343,144,8,62,403,344,145,6,60,404,342,146,7,61,402,154,338,69,1,398,155,336,70,0,396,153,337,71,2,397,150,341,68,3,401,151,339,66,4,399,152,340,67,5,400,667,677,679,674,647,645,652,84,646,607,605,85,612,606,86,625,627,632,626,565,567,87,572,566,585,587,88,592,586,545,547,89,552,546,467,465,472,90,466,426,437,439,91,438,447,445,452,92,446,527,525,532,93,526,487,485,492,94,486,507,505,512,95,506,696,691,701,685,659,657,640,250,655,619,617,251,600,615,249,637,639,620,635,577,579,246,561,575,597,599,247,581,595,557,559,248,541,555,479,477,461,241,475,420,435,422,242,433,459,457,441,240,455,539,537,521,244,535,499,497,480,245,495,519,517,501,243,515,692,699,689,686,648,649,653,45,654,608,609,46,613,614,47,629,628,633,634,569,568,44,573,574,589,588,42,593,594,549,548,43,553,554,468,469,473,36,474,427,428,431,37,432,448,449,453,38,454,528,529,533,39,534,488,489,493,40,494,508,509,513,41,514,690,697,703,693,119,30,323,214,164,117,31,215,321,162,213,32,118,322,163,33,115,210,319,167,34,116,211,320,165,35,114,212,318,166,110,28,314,205,159,108,29,312,206,160,109,27,313,204,161,113,24,317,208,158,111,25,315,209,156,112,26,316,207,157,683,681,676,665,287,335,56,239,265,285,333,237,54,266,238,334,286,55,264,331,283,235,59,268,332,284,236,57,269,330,282,234,58,267,278,326,51,230,271,276,324,52,228,272,277,325,53,229,270,281,329,50,233,274,279,327,48,231,275,280,328,49,232,273,666,662,661,684,311,359,371,140,395,309,357,138,369,393,139,358,310,370,394,355,307,143,367,391,356,308,141,368,392,354,306,142,366,390,302,350,362,135,386,300,348,360,136,384,301,349,361,137,385,305,353,365,134,389,303,351,363,132,387,304,352,364,133,388,668,675,664,671,202,170,383,123,181,203,168,124,381,182,125,169,201,382,180,173,198,122,379,184,171,199,120,380,185,172,200,121,378,183,193,176,374,129,187,194,174,372,130,188,192,175,373,131,186,196,179,377,128,190,197,177,375,126,191,195,178,376,127,189,678,673,682,672 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#e6bbf558fb3ffab686d395ed44cee4ecb6da0873fc29bc1527bdf36d2fd1603f, 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 21:18:17 · history