Equation 677 Database

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Magma f1e0ed5cb3ae…

magma f1e0ed5cb3ae
Size
705
Isomorphism class hash
f1e0ed5cb3aea576086535cf5bc96730b5ce56b83ac3d935a2c3cc0d0373ba6d
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 18:12:40
Display reorder
660,221,202,61,266,215,222,200,267,62,216,223,201,268,60,217,220,205,269,57,214,203,218,270,58,212,204,219,271,59,213,227,197,67,272,206,228,198,68,273,207,229,199,66,274,208,226,196,63,275,209,224,194,64,276,210,225,195,65,277,211,685,686,688,687,157,192,178,371,142,155,193,372,176,140,156,191,373,177,141,153,188,370,181,145,189,154,368,179,143,190,152,369,180,144,148,183,173,362,137,146,184,174,363,138,147,182,175,364,139,151,186,172,365,136,149,187,170,366,134,150,185,171,367,135,701,702,704,703,604,581,616,261,592,605,582,262,617,593,606,580,260,618,594,607,584,264,619,595,585,608,265,620,596,583,609,263,621,597,610,587,622,259,598,611,588,623,257,599,612,586,624,258,600,613,590,625,255,601,614,591,626,256,602,615,589,627,254,603,670,669,672,671,380,403,396,8,158,381,401,6,397,159,382,402,7,395,160,383,399,11,392,161,400,384,9,393,162,398,385,10,394,163,378,409,387,3,164,379,407,388,4,165,377,408,386,5,166,374,405,390,2,167,375,406,391,1,168,376,404,389,0,169,680,677,679,678,434,412,446,81,422,435,410,82,447,423,436,411,83,448,424,437,415,84,449,425,413,438,85,450,426,414,439,86,451,427,440,418,452,87,428,441,416,453,88,429,442,417,454,89,430,443,421,455,90,431,444,419,456,91,432,445,420,457,92,433,689,690,691,692,530,508,542,109,518,531,506,110,543,519,532,507,108,544,520,533,511,105,545,521,509,534,106,546,522,510,535,107,547,523,536,514,548,115,524,537,512,549,116,525,538,513,550,114,526,539,517,551,111,527,540,515,552,112,528,541,516,553,113,529,697,698,700,699,634,24,651,14,75,635,25,12,649,76,636,26,13,650,77,637,27,17,647,78,28,638,15,648,79,29,639,16,646,80,632,30,642,20,73,633,31,640,18,74,631,32,641,19,72,628,33,645,23,69,629,34,643,21,70,630,35,644,22,71,661,662,664,663,302,280,316,238,290,303,278,236,314,291,304,279,237,315,292,305,283,241,319,293,281,306,239,317,294,282,307,240,318,295,308,286,322,233,296,309,284,320,234,297,310,285,321,235,298,311,289,325,232,299,312,287,323,230,300,313,288,324,231,301,682,681,684,683,566,557,579,244,41,564,558,242,577,39,565,559,243,578,40,569,556,247,575,44,554,567,245,576,42,555,568,246,574,43,656,658,659,250,657,117,563,570,248,121,653,652,654,249,655,120,562,573,253,38,118,560,571,251,36,119,561,572,252,37,693,694,696,695,471,494,483,95,460,472,495,93,484,458,470,496,94,482,459,474,497,98,486,463,498,475,96,487,461,499,473,97,485,462,477,500,489,101,466,478,501,490,99,464,476,502,488,100,465,480,503,492,104,469,481,504,493,102,467,479,505,491,103,468,666,665,668,667,332,353,347,51,129,333,354,52,348,130,334,355,53,349,128,335,352,54,346,132,350,336,55,344,133,351,337,56,345,131,330,359,338,49,127,331,360,339,50,125,329,361,340,48,126,326,358,341,45,123,327,356,342,46,124,328,357,343,47,122,674,673,676,675 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#6b720d896a29843112ad3c0147d655cf7bb7a1ca51519c2978dbef59d093ebaf, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 18:12:42 · history