Equation 677 Database

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Magma c54c9ebd1fd4…

magma c54c9ebd1fd4
Size
705
Isomorphism class hash
c54c9ebd1fd42c742d1c255889c5c30d1bf0cb5efd887598fcbe0da36b518dc9
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 19:58:19
Display reorder
660,185,184,183,180,181,182,190,191,189,186,187,188,166,167,165,162,163,164,157,158,156,160,161,159,150,151,152,153,154,155,148,149,147,144,145,146,408,409,410,411,412,413,414,415,416,417,418,419,176,174,175,179,177,178,171,172,173,170,168,169,675,685,678,691,562,561,563,560,558,559,552,553,554,555,556,557,532,533,531,528,529,530,538,539,537,534,535,536,521,519,520,517,518,516,527,525,526,523,524,522,18,19,20,21,22,23,16,17,15,12,13,14,541,542,540,544,545,543,547,548,546,550,551,549,687,699,693,703,52,51,53,50,48,49,57,58,59,56,54,55,132,133,134,135,136,137,138,139,140,141,142,143,129,130,131,128,126,127,120,121,122,123,124,125,399,400,401,398,396,397,405,406,407,404,402,403,44,42,43,47,45,46,39,40,41,38,36,37,669,670,667,682,598,597,599,596,594,595,588,589,590,591,592,593,568,569,567,564,565,566,574,575,573,570,571,572,601,602,600,604,605,603,607,608,606,610,611,609,28,29,27,24,25,26,34,35,33,30,31,32,577,578,576,580,581,579,583,584,582,586,587,585,674,683,681,694,657,659,658,655,656,654,650,648,649,653,651,652,630,631,632,633,634,635,628,629,627,624,625,626,612,613,614,615,616,617,618,619,620,621,622,623,283,284,282,286,287,285,281,279,280,277,278,276,645,646,647,644,642,643,636,637,638,639,640,641,690,697,695,704,383,382,381,378,379,380,373,374,372,376,377,375,351,352,353,350,348,349,357,358,359,356,354,355,341,339,340,337,338,336,347,345,346,343,344,342,267,268,269,266,264,265,273,274,275,272,270,271,361,362,360,364,365,363,367,368,366,370,371,369,689,700,688,701,257,256,255,252,253,254,262,263,261,258,259,260,230,228,229,233,231,232,236,234,235,239,237,238,219,220,221,218,216,217,225,226,227,224,222,223,214,215,213,210,211,212,205,206,204,208,209,207,243,244,245,242,240,241,249,250,251,248,246,247,662,661,663,673,457,456,458,459,460,461,462,463,464,465,466,467,432,433,434,435,436,437,438,439,440,441,442,443,421,422,420,424,425,423,427,428,426,430,431,429,86,84,85,89,87,88,92,90,91,95,93,94,448,449,447,444,445,446,454,455,453,450,451,452,676,684,679,692,66,68,67,71,69,70,63,64,65,62,60,61,392,390,391,395,393,394,387,388,389,386,384,385,76,77,75,72,73,74,82,83,81,78,79,80,112,113,111,108,109,110,118,119,117,114,115,116,197,195,196,193,194,192,203,201,202,199,200,198,686,698,696,702,305,304,303,300,301,302,310,311,309,306,307,308,324,325,326,327,328,329,330,331,332,333,334,335,313,314,312,316,317,315,319,320,318,322,323,321,6,7,8,9,10,11,4,5,3,1,0,2,291,292,293,290,288,289,297,298,299,296,294,295,664,671,666,677,497,496,495,492,493,494,502,503,501,498,499,500,470,468,469,473,471,472,476,474,475,479,477,478,506,504,505,509,507,508,512,510,511,515,513,514,104,102,103,107,105,106,99,100,101,98,96,97,483,484,485,482,480,481,489,490,491,488,486,487,665,672,668,680 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, 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 19:58:20 · history