Equation 677 Database

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Magma 67a01a4491f2…

magma 67a01a4491f2
Size
705
Isomorphism class hash
67a01a4491f257f5419206c5a0fbfe842ebd2df0355df1ca53e74c8f1e6779d4
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 16:23:37
Display reorder
660,23,214,600,67,197,21,215,598,68,195,22,213,599,66,196,19,217,603,70,200,218,20,601,71,198,69,18,216,602,199,595,14,220,65,192,596,12,221,63,193,597,13,219,64,194,17,594,223,61,191,15,592,224,62,189,16,593,222,60,190,687,688,686,685,371,163,389,402,390,369,164,387,403,391,370,162,388,404,392,367,159,385,405,393,160,368,386,406,394,407,366,161,384,395,380,377,154,408,396,378,375,155,409,397,379,376,153,410,398,373,383,157,411,399,374,381,158,412,400,372,382,156,413,401,703,704,701,702,560,204,579,547,580,561,205,577,548,581,559,206,578,549,582,556,203,575,546,583,201,557,576,544,584,545,558,202,574,585,570,566,210,553,586,568,567,211,554,587,569,565,212,555,588,562,573,209,552,589,563,571,207,550,590,564,572,208,551,591,671,672,670,669,8,283,420,42,171,6,281,421,43,172,7,282,422,44,173,11,286,423,45,174,284,9,424,46,175,47,10,285,425,176,418,3,289,40,169,419,4,287,41,170,417,5,288,39,168,2,414,292,36,165,1,415,290,37,166,0,416,291,38,167,679,680,678,677,465,51,428,453,441,466,52,426,454,442,467,53,427,455,443,464,50,431,452,440,48,462,429,450,438,451,463,49,430,439,434,471,57,459,447,432,472,58,460,448,433,473,59,461,449,470,437,56,458,446,468,435,54,456,444,469,436,55,457,445,692,691,690,689,254,185,270,309,530,252,183,271,310,528,253,184,272,308,529,250,188,269,305,533,186,251,267,306,531,307,249,187,268,532,261,260,180,315,525,262,258,181,316,526,263,259,182,314,527,256,264,179,311,524,257,265,177,312,522,255,266,178,313,523,699,700,698,697,131,82,88,109,107,129,83,89,110,105,130,81,87,108,106,127,78,84,112,103,79,128,85,113,104,111,126,80,86,102,94,122,73,115,98,95,120,74,116,96,93,121,72,114,97,125,90,76,118,101,123,91,77,119,99,124,92,75,117,100,663,664,662,661,628,227,642,616,604,629,225,640,617,605,630,226,641,618,606,631,230,645,619,607,228,632,643,620,608,621,633,229,644,609,648,634,233,622,610,646,635,231,623,611,647,636,232,624,612,637,651,236,625,613,638,649,234,626,614,639,650,235,627,615,682,683,684,681,541,31,329,324,139,542,32,327,325,140,540,30,328,323,138,543,34,273,326,280,35,654,653,652,655,658,659,33,656,657,276,539,29,322,137,274,537,27,320,135,275,538,28,321,136,535,279,25,318,133,536,277,26,319,134,534,278,24,317,132,695,696,693,694,501,293,514,489,477,502,294,515,490,478,503,295,513,491,479,500,296,510,488,476,297,498,511,486,474,487,499,298,512,475,520,507,299,495,483,521,508,300,496,484,519,509,301,497,485,506,516,302,494,482,504,517,303,492,480,505,518,304,493,481,667,668,665,666,243,144,337,359,344,244,145,338,357,342,245,146,336,358,343,246,143,340,355,347,141,247,341,356,345,354,248,142,339,346,335,241,150,365,350,333,242,151,363,348,334,240,152,364,349,237,331,149,361,353,238,332,147,362,351,239,330,148,360,352,675,676,673,674 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#2fbfbc696f8770de67b632f9354275e3bbc4952318d0e644426634c23ae4ab08, 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 16:23:39 · history