Equation 677 Database

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Magma 10b76be30e27…

magma 10b76be30e27
Size
705
Isomorphism class hash
10b76be30e27a59ce1cc41da6f10cc0dc883f1396afc6ca4ec15cc06371cb63a
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 19:20:27
Display reorder
660,489,62,486,487,485,509,60,507,506,505,527,61,529,526,525,58,469,466,467,465,59,432,430,431,428,57,449,446,447,444,609,53,605,607,606,629,51,625,627,626,649,52,645,647,646,589,56,585,587,586,549,54,545,547,546,569,55,565,567,566,686,687,685,690,493,109,494,484,488,513,110,504,514,508,524,108,533,535,528,105,473,475,464,468,106,437,438,436,424,107,453,455,443,448,613,100,614,604,608,633,101,635,624,628,653,99,655,644,648,593,103,597,584,588,553,104,556,544,548,573,102,577,564,568,688,694,700,692,121,5,335,371,407,122,3,372,336,408,373,4,120,337,409,8,117,334,370,406,6,118,332,368,404,7,119,333,369,405,112,11,341,377,413,113,9,342,378,414,111,10,343,379,415,115,14,340,376,412,116,12,338,374,410,114,13,339,375,411,680,672,667,669,76,24,311,204,246,77,25,205,312,247,203,26,75,313,245,23,79,310,200,242,21,80,308,201,243,22,78,309,202,244,82,15,317,210,237,83,16,318,211,238,81,17,319,209,236,85,18,316,206,240,86,19,314,207,241,84,20,315,208,239,678,677,665,673,490,32,481,495,491,510,30,515,500,511,534,31,530,520,531,28,470,460,474,471,29,425,423,427,426,27,450,440,454,451,610,38,600,615,611,630,36,621,634,631,650,37,641,654,651,590,34,580,596,591,550,35,541,557,551,570,33,560,576,571,693,701,696,691,499,264,497,498,482,519,265,518,517,502,537,263,539,538,522,260,479,478,477,462,261,422,420,421,429,262,459,458,457,445,619,270,617,618,602,637,271,639,638,622,659,269,658,657,642,599,266,595,594,582,559,267,555,554,542,579,268,575,574,562,699,704,698,689,480,257,496,483,492,501,258,503,516,512,523,259,521,536,532,256,461,476,463,472,254,434,439,435,433,255,441,456,442,452,601,248,616,603,612,620,249,636,623,632,640,250,656,643,652,581,251,598,583,592,540,252,558,543,552,561,253,578,563,572,697,703,702,695,299,98,395,171,166,300,96,172,396,167,173,97,301,397,165,94,298,394,174,169,95,296,392,175,170,93,297,393,176,168,305,89,401,177,164,306,87,402,417,162,307,88,403,418,163,304,92,400,178,160,302,90,398,179,161,303,91,399,180,159,683,682,679,663,359,278,323,127,347,360,279,128,324,348,126,280,361,325,349,281,358,322,123,346,282,356,320,124,344,283,357,321,125,345,365,276,329,133,353,366,277,330,134,354,367,275,331,132,355,364,272,328,129,352,362,273,326,130,350,363,274,327,131,351,668,664,666,684,198,73,383,225,216,199,74,226,384,217,224,72,197,385,215,69,194,382,228,212,70,195,380,229,213,71,196,381,227,214,189,64,389,231,222,190,65,390,232,223,188,63,391,230,221,192,67,388,234,218,193,68,386,235,219,191,66,387,233,220,671,670,675,676,156,46,183,137,287,157,47,135,184,288,136,45,158,182,289,49,155,186,140,286,50,153,187,138,284,48,154,185,139,285,147,44,181,143,293,148,42,416,141,294,149,43,419,142,295,150,40,0,146,292,151,41,2,144,290,152,39,1,145,291,661,674,681,662 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#9f23da9903d6ebc1c6f98cbe23264669be86f8e7144737b42fbccbf8aeddcd62, 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 19:20:28 · history