Equation 677 Database

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Magma 3196e49eb705…

magma 3196e49eb705
Size
705
Isomorphism class hash
3196e49eb70503ae4a198bcf55cdb89b13f314e710ef7d426648a5285fbca1bb
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 17:34:49
Display reorder
660,567,587,63,213,558,568,585,64,214,559,65,569,215,560,586,566,62,583,212,561,564,60,584,210,562,565,61,582,211,563,578,69,204,573,556,576,70,205,574,557,577,71,206,575,555,68,581,207,572,552,66,579,208,570,553,67,580,209,571,554,687,688,686,685,363,382,344,306,349,364,383,342,307,350,343,365,308,348,381,362,347,378,309,352,360,345,379,310,353,361,346,380,311,351,373,339,304,369,355,374,340,305,370,356,372,341,303,371,354,338,376,300,368,358,336,377,301,366,359,337,375,302,367,357,703,704,701,702,195,157,173,540,182,196,158,171,541,180,172,197,542,181,156,194,169,160,543,185,192,170,161,544,183,193,168,159,545,184,163,179,546,201,188,164,177,547,202,186,162,178,548,203,187,175,166,549,200,191,176,167,550,198,189,174,165,551,199,190,671,672,670,669,399,418,40,219,390,400,419,41,220,391,39,401,221,392,417,398,36,414,218,393,396,37,415,216,394,397,38,416,217,395,409,46,225,405,388,410,47,226,406,389,408,45,227,407,387,42,412,224,404,384,43,413,222,402,385,44,411,223,403,386,679,680,678,677,432,446,461,57,420,433,444,459,58,421,460,434,59,422,445,435,457,449,56,423,436,458,447,54,424,437,456,448,55,425,452,467,48,438,426,450,465,49,439,427,451,466,50,440,428,463,455,51,441,429,464,453,52,442,430,462,454,53,443,431,692,691,690,689,246,255,273,138,522,247,256,274,139,523,275,248,140,524,257,249,272,254,141,525,250,270,252,142,526,251,271,253,143,527,261,264,136,244,520,262,265,137,245,521,263,266,135,243,519,267,260,132,240,516,268,258,133,241,517,269,259,134,242,518,699,700,698,697,95,15,33,0,79,93,16,34,2,80,35,94,1,78,17,91,32,14,4,82,92,30,12,5,83,90,31,13,3,81,21,24,7,86,77,22,25,8,84,75,23,26,6,85,76,27,20,10,89,73,28,18,11,87,74,29,19,9,88,72,663,664,662,661,612,626,596,277,600,613,624,594,278,601,595,614,276,602,625,615,599,629,280,603,616,597,627,281,604,617,598,628,279,605,632,591,283,618,606,630,592,284,619,607,631,593,282,620,608,590,635,286,621,609,588,633,287,622,610,589,634,285,623,611,682,683,684,681,650,651,649,104,648,654,655,653,102,652,656,658,103,657,659,644,646,647,107,645,637,636,638,105,639,642,640,643,106,641,538,154,99,532,148,539,155,100,533,149,537,153,101,531,147,150,534,98,528,144,151,535,96,529,145,152,536,97,530,146,695,696,693,694,494,508,470,231,485,492,509,468,232,483,469,493,233,484,507,497,473,504,230,481,495,471,505,228,482,496,472,506,229,480,514,476,237,500,491,515,474,238,498,489,513,475,239,499,490,479,510,236,503,487,477,511,234,501,488,478,512,235,502,486,667,668,665,666,121,319,335,291,116,122,320,333,292,114,334,120,293,115,318,124,331,322,290,119,125,332,323,288,117,123,330,321,289,118,317,326,297,127,111,315,324,298,128,112,316,325,299,126,113,329,313,296,130,110,327,314,294,131,108,328,312,295,129,109,675,676,673,674 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#59c0dab3d55e83047c113809dcb6925b23956e0c747f2365bb6fbba97ebd5493, 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 17:34:50 · history