Equation 677 Database

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Magma c951842391cd…

magma c951842391cd
Size
705
Isomorphism class hash
c951842391cdeb95a2be6b66d2ccdffd95ea1e7ed1c4d00dc3c512b2a96e5dc8
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 19:14:35
Display reorder
660,23,525,533,523,531,21,485,493,483,491,22,505,513,503,511,449,19,453,447,452,464,20,471,462,470,424,18,431,423,430,653,645,14,643,651,613,605,12,603,611,633,625,13,623,631,565,573,17,563,571,585,593,15,583,591,545,553,16,543,551,702,693,698,687,181,524,535,529,526,182,484,495,489,486,180,504,515,509,506,448,184,446,444,442,463,185,473,468,465,421,183,433,428,425,655,644,187,649,646,615,604,188,609,606,635,624,186,629,626,564,575,190,569,566,584,595,191,589,586,544,555,189,549,546,691,689,699,685,164,9,334,54,341,162,10,335,55,339,163,11,333,56,340,8,167,330,57,337,6,165,331,58,338,7,166,332,59,336,325,1,159,52,347,326,0,160,53,345,324,2,161,51,346,3,328,158,48,343,4,329,156,49,344,5,327,157,50,342,679,667,662,677,73,265,281,115,215,74,266,279,116,213,72,264,280,114,214,268,76,277,118,211,269,77,278,119,212,267,75,276,117,210,287,271,79,113,206,285,272,80,111,204,286,270,78,112,205,274,283,82,109,209,275,284,83,110,207,273,282,81,108,208,670,675,669,683,37,536,537,527,538,38,496,497,487,498,36,516,517,507,518,456,40,454,450,455,478,41,474,466,475,436,39,434,426,435,657,656,43,647,658,617,616,44,607,618,637,636,42,627,638,576,577,46,567,578,596,597,47,587,598,556,557,45,547,558,694,703,701,696,66,530,521,532,539,67,490,480,492,499,68,510,501,512,519,451,69,457,458,459,469,70,476,477,479,429,71,437,438,439,640,650,64,652,659,601,610,65,612,619,620,630,63,632,639,570,561,60,572,579,590,581,61,592,599,550,540,62,552,559,695,700,686,692,89,520,528,522,534,87,481,488,482,494,88,500,508,502,514,440,85,443,441,445,461,86,467,460,472,422,84,427,420,432,648,641,95,642,654,608,600,93,602,614,628,621,94,622,634,560,568,91,562,574,580,588,92,582,594,541,548,90,542,554,704,697,690,688,175,377,200,293,305,176,375,198,291,303,174,376,199,292,304,373,178,203,289,301,374,179,201,290,302,372,177,202,288,300,195,383,173,299,311,196,381,171,297,309,197,382,172,298,310,379,194,169,295,307,380,192,170,296,308,378,193,168,294,306,663,664,682,674,30,413,249,224,120,31,411,250,222,121,32,412,251,223,122,409,33,248,227,123,410,34,246,225,124,408,35,247,226,125,240,419,28,219,126,241,417,29,220,127,242,418,27,221,128,415,243,24,218,129,416,244,25,216,130,414,245,26,217,131,665,673,671,684,153,401,98,317,389,154,399,96,315,387,155,400,97,316,388,397,152,101,313,385,398,150,99,314,386,396,151,100,312,384,104,407,144,323,395,102,405,145,321,393,103,406,146,322,394,403,107,147,319,391,404,105,148,320,392,402,106,149,318,390,666,676,680,678,230,353,257,140,365,228,351,255,138,363,229,352,256,139,364,349,233,253,143,361,350,231,254,141,362,348,232,252,142,360,263,359,236,135,371,261,357,234,136,369,262,358,235,137,370,355,259,239,134,367,356,260,237,132,368,354,258,238,133,366,681,672,661,668 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#9613877152071542ba1176ebd2d9075b5c9b63b690264e2f5c72257d6a275b00, 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 19:14:36 · history