Equation 677 Database

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Magma 4f4273fada1b…

magma 4f4273fada1b
Size
705
Isomorphism class hash
4f4273fada1b0ee658d726698932c5711b595caf51ab1bf671be6971c2839218
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 15:02:25
Display reorder
660,99,615,601,612,602,100,622,635,621,632,101,642,655,640,652,98,595,582,580,592,96,555,542,541,552,97,575,562,561,572,420,105,422,435,432,441,106,443,453,450,461,107,462,475,472,104,481,482,495,492,102,501,502,515,512,103,520,522,535,532,688,685,687,694,138,603,600,613,604,139,624,623,620,633,140,644,643,641,653,141,583,584,581,593,142,543,544,540,553,143,563,564,560,573,421,136,424,423,433,442,137,445,444,451,460,135,464,463,473,132,480,484,483,493,133,500,504,503,513,134,521,524,523,533,696,704,690,700,200,333,123,1,154,198,155,334,124,0,199,153,335,125,2,203,332,150,122,3,201,330,151,120,4,202,331,152,121,5,129,195,145,324,6,130,196,146,325,7,131,197,144,326,8,194,128,148,327,9,192,126,149,328,10,193,127,147,329,11,667,678,682,669,53,28,238,80,357,51,358,29,239,78,52,359,27,237,79,49,24,356,234,83,50,25,354,235,81,48,26,355,236,82,229,59,348,34,75,230,57,349,35,76,228,58,350,33,77,55,232,351,30,74,56,233,352,31,72,54,231,353,32,73,666,675,672,670,255,606,616,605,608,256,628,626,636,625,257,648,646,656,645,254,586,588,596,585,252,546,548,556,545,253,566,568,576,565,436,261,428,426,425,454,262,459,458,457,476,263,468,466,465,260,496,488,486,485,258,516,508,506,505,259,536,528,526,525,697,692,695,702,23,617,619,611,614,21,634,637,639,631,22,654,657,659,651,19,597,594,599,591,20,557,554,559,551,18,577,574,579,571,439,14,434,437,431,440,12,452,455,449,479,13,474,477,471,17,499,494,497,491,15,519,514,517,511,16,539,534,537,531,701,693,691,698,88,609,610,607,618,89,638,629,630,627,87,658,649,650,647,84,589,598,590,587,85,549,558,550,547,86,569,578,570,567,430,94,438,429,427,448,95,456,447,446,470,93,478,469,467,90,490,498,489,487,91,510,518,509,507,92,530,538,529,527,699,689,686,703,68,345,209,217,321,66,322,346,207,218,67,323,347,208,216,71,344,320,205,220,69,342,318,206,221,70,343,319,204,219,215,63,312,336,223,213,64,313,337,224,214,65,314,338,222,62,211,315,339,226,60,212,316,340,227,61,210,317,341,225,668,673,662,665,185,109,309,369,289,183,290,110,310,370,184,288,108,311,371,181,112,292,308,368,182,113,293,306,366,180,111,291,307,367,300,191,295,115,360,301,189,296,116,361,302,190,294,114,362,187,303,298,118,363,188,304,299,119,364,186,305,297,117,365,684,664,674,679,163,381,285,417,265,164,266,382,286,418,162,264,383,287,419,166,380,268,284,416,167,378,269,282,414,165,379,267,283,415,276,161,271,372,408,277,159,272,373,409,278,160,270,374,410,157,279,274,375,411,158,280,275,376,412,156,281,273,377,413,676,663,683,661,246,43,178,393,405,247,406,44,179,394,248,407,42,177,395,249,46,404,174,392,250,47,402,175,390,251,45,403,176,391,169,244,396,41,384,170,245,397,39,385,168,243,398,40,386,240,172,399,37,387,241,173,400,38,388,242,171,401,36,389,671,681,677,680 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#003b1571ae5bf3b67323fc5b960381c29f1c759a7de9437dd38ba69e115a500f, 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 15:02:26 · history