Equation 677 Database

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Magma c60f4902ccb1…

magma c60f4902ccb1
Size
705
Isomorphism class hash
c60f4902ccb121b986fc5f15c9c1469f7156f52b9ef6a9d698bb4afccdc1a176
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 19:11:17
Display reorder
660,460,462,208,472,464,209,428,432,420,422,440,442,207,453,444,204,521,533,522,524,480,205,493,482,484,206,501,513,502,504,581,214,593,582,584,540,215,553,542,544,561,213,573,562,564,210,640,653,642,644,211,601,613,602,604,212,620,633,622,624,687,692,689,691,468,465,0,466,467,2,426,424,423,425,449,446,1,447,448,4,529,527,526,528,489,5,487,486,488,3,509,507,506,508,589,7,587,586,588,549,8,547,546,548,569,6,567,566,568,10,649,647,646,648,11,609,607,606,608,9,629,627,626,628,685,686,696,693,314,57,107,71,278,105,312,69,58,276,313,59,106,70,277,103,317,67,56,281,315,104,68,54,279,102,316,66,55,280,320,98,62,48,284,318,96,60,49,282,319,97,61,50,283,101,323,65,51,287,99,321,63,52,285,100,322,64,53,286,666,669,663,667,266,237,146,251,410,144,264,249,238,408,265,239,145,250,409,149,269,247,236,413,267,147,248,234,411,148,268,246,235,412,272,152,242,228,416,270,150,240,229,414,271,151,241,230,415,155,275,245,231,419,153,273,243,232,417,154,274,244,233,418,661,681,683,672,473,470,253,474,471,254,433,434,430,431,457,451,252,458,452,256,537,538,531,532,497,257,498,491,492,255,517,518,511,512,597,259,598,591,592,557,260,558,551,552,577,258,578,571,572,262,657,658,651,652,263,617,618,611,612,261,637,638,631,632,699,701,694,702,476,478,227,477,479,225,438,436,439,437,455,456,226,454,445,223,534,535,536,525,494,224,495,496,485,222,514,515,516,505,594,218,595,596,585,554,216,555,556,545,574,217,575,576,565,221,654,655,656,645,219,614,615,616,605,220,634,635,636,625,703,695,700,698,469,461,14,463,475,12,427,421,429,435,450,441,13,443,459,17,530,523,520,539,490,15,483,481,499,16,510,503,500,519,590,20,583,580,599,550,18,543,541,559,570,19,563,560,579,23,650,643,641,659,21,610,603,600,619,22,630,623,621,639,688,690,704,697,73,94,36,163,177,37,74,164,95,178,72,93,38,162,179,39,76,166,90,176,77,40,167,91,174,41,75,165,92,175,79,42,161,85,168,80,43,159,86,169,78,44,160,84,170,45,82,157,88,171,46,83,158,89,172,47,81,156,87,173,673,677,674,678,340,135,32,398,194,30,337,396,136,192,339,137,31,397,193,35,346,401,134,197,342,33,399,132,195,34,344,400,133,196,353,27,404,141,200,349,28,402,142,198,351,29,403,143,199,26,359,407,140,203,24,355,405,138,201,25,357,406,139,202,670,682,680,684,386,362,115,341,302,116,384,336,360,300,385,361,114,338,301,118,389,347,365,305,387,119,343,363,303,117,388,345,364,304,392,113,352,368,308,390,111,348,366,306,391,112,350,367,307,109,395,358,371,311,110,393,354,369,309,108,394,356,370,310,679,671,665,675,188,326,129,290,374,130,186,288,324,372,187,325,131,289,373,128,191,293,329,377,189,126,291,327,375,127,190,292,328,376,183,120,296,332,380,184,121,294,330,378,185,122,295,331,379,123,182,299,335,383,124,180,297,333,381,125,181,298,334,382,662,664,676,668 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#8ecda3bf937b7c39d65eafcd0523fd56cf367f983a83102877b0cefff256addf, 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 19:11:18 · history