Equation 677 Database

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Magma ad1984c0e200…

magma ad1984c0e200
Size
705
Isomorphism class hash
ad1984c0e200deea09cc101a8436aca6ad2ecd978e0939d53fd67efe0147e0fa
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 16:48:21
Display reorder
660,633,632,22,628,629,653,652,23,648,649,613,612,21,608,609,552,553,18,548,549,19,573,572,568,569,592,593,20,588,589,451,450,13,447,448,475,474,14,469,470,435,434,12,429,430,514,515,16,509,510,532,533,17,528,529,494,495,15,489,490,690,686,697,698,634,635,43,624,623,654,655,44,644,643,614,615,42,604,603,555,554,46,544,543,47,574,575,564,563,595,594,45,584,583,452,453,41,446,445,476,477,39,465,464,436,437,40,425,424,517,516,37,505,504,535,534,38,524,523,497,496,36,485,484,694,695,702,700,418,406,200,334,310,419,407,198,335,311,417,405,199,333,309,402,414,203,330,306,201,415,403,331,307,404,416,202,332,308,409,397,195,325,301,410,398,196,326,302,408,396,197,324,300,400,412,194,328,304,401,413,192,329,305,399,411,193,327,303,667,664,679,680,382,394,167,126,370,383,395,165,127,371,381,393,166,128,369,390,378,163,129,366,164,379,391,130,367,392,380,162,131,368,373,385,158,124,361,374,386,156,125,362,372,384,157,123,360,388,376,161,120,364,389,377,159,121,365,387,375,160,122,363,661,671,677,675,639,638,205,630,620,659,658,206,650,640,619,618,204,610,601,558,559,208,550,541,209,579,578,570,561,598,599,207,590,581,458,459,211,449,444,478,479,212,471,462,438,439,210,431,422,519,518,214,511,502,539,538,215,530,521,499,498,213,491,482,691,689,688,701,627,622,285,626,631,647,642,286,646,651,607,602,287,606,611,542,547,284,546,551,282,567,562,566,571,582,587,283,586,591,457,456,276,440,441,468,463,277,467,472,428,423,278,427,432,503,508,279,507,512,522,527,280,526,531,483,488,281,487,492,687,692,693,696,625,637,115,621,636,645,656,116,641,657,605,617,114,600,616,557,545,118,540,556,119,565,577,560,576,596,585,117,580,597,454,455,113,443,442,466,473,111,460,461,426,433,112,421,420,513,506,109,501,500,537,525,110,520,536,493,486,108,481,480,699,704,703,685,87,298,217,184,171,88,299,218,185,172,89,297,216,183,173,294,86,220,180,170,221,84,295,181,168,296,85,219,182,169,93,289,223,190,177,94,290,224,191,178,95,288,222,189,179,292,92,226,186,176,293,90,227,187,174,291,91,225,188,175,678,676,663,672,322,24,9,98,358,323,25,10,96,359,321,26,11,97,357,27,318,8,101,354,6,319,28,99,355,29,320,7,100,356,313,30,1,104,349,314,31,0,102,350,312,32,2,103,348,33,316,3,107,352,34,317,4,105,353,35,315,5,106,351,682,670,668,665,149,76,265,138,66,147,77,266,139,67,148,75,264,140,68,72,145,268,141,69,269,146,73,142,70,74,144,267,143,71,155,82,271,136,64,153,83,272,137,65,154,81,270,135,63,78,151,274,132,60,79,152,275,133,61,80,150,273,134,62,684,681,666,683,239,251,54,346,262,237,249,55,347,263,238,250,56,345,261,247,235,57,342,258,58,236,248,343,259,246,234,59,344,260,230,242,52,337,253,228,240,53,338,254,229,241,51,336,252,245,233,48,340,256,243,231,49,341,257,244,232,50,339,255,669,662,674,673 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#3f4c16e16e9bd422beeb4e3c1331ed0b07b0ac931af0d47b2d7497fadfe20a6b, 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 16:48:22 · history