Equation 677 Database

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Magma 282e867fca45…

magma 282e867fca45
Size
705
Isomorphism class hash
282e867fca458ec493be4fc18510e218b55281f415ee48a39a91af40f66b2816
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 20:01:41
Display reorder
704,191,190,189,186,187,188,181,182,180,184,185,183,200,198,199,203,201,202,195,196,197,194,192,193,14,12,13,17,15,16,20,18,19,23,21,22,171,172,173,170,168,169,177,178,179,176,174,175,78,79,80,81,82,83,76,77,75,72,73,74,677,683,684,687,404,403,402,406,407,405,401,399,400,397,398,396,410,408,409,413,411,412,416,414,415,419,417,418,422,420,421,425,423,424,428,426,427,431,429,430,443,441,442,439,440,438,434,432,433,437,435,436,85,86,84,88,89,87,91,92,90,94,95,93,691,697,699,703,640,639,641,638,636,637,645,646,647,644,642,643,607,608,606,610,611,609,605,603,604,601,602,600,620,618,619,623,621,622,615,616,617,614,612,613,631,632,630,634,635,633,629,627,628,625,626,624,320,318,319,323,321,322,315,316,317,314,312,313,664,670,675,669,447,449,448,445,446,444,455,453,454,451,452,450,465,466,467,464,462,463,456,457,458,459,460,461,477,478,479,476,474,475,468,469,470,471,472,473,485,483,484,481,482,480,491,489,490,487,488,486,365,363,364,361,362,360,371,369,370,367,368,366,676,682,686,679,525,527,526,523,524,522,518,516,517,521,519,520,532,533,531,528,529,530,538,539,537,534,535,536,503,501,502,499,500,498,494,492,493,497,495,496,505,506,504,508,509,507,511,512,510,514,515,513,383,381,382,379,380,378,374,372,373,377,375,376,690,696,702,700,650,649,648,652,653,651,655,656,654,658,659,657,582,583,584,585,586,587,580,581,579,576,577,578,334,335,333,330,331,332,325,326,324,328,329,327,10,11,9,6,7,8,0,2,1,4,5,3,554,552,553,557,555,556,560,558,559,563,561,562,689,692,698,693,142,141,143,140,138,139,132,133,134,135,136,137,144,145,146,147,148,149,150,151,152,153,154,155,110,108,109,113,111,112,116,114,115,119,117,118,129,130,131,128,126,127,120,121,122,123,124,125,161,159,160,157,158,156,167,165,166,163,164,162,660,662,663,661,47,46,45,42,43,44,37,38,36,40,41,39,211,212,210,214,215,213,209,207,208,205,206,204,224,222,223,227,225,226,219,220,221,218,216,217,235,236,234,238,239,237,233,231,232,229,230,228,107,105,106,103,104,102,98,96,97,101,99,100,678,681,685,680,298,297,299,296,294,295,288,289,290,291,292,293,300,301,302,303,304,305,306,307,308,309,310,311,270,271,272,273,274,275,268,269,267,264,265,266,279,280,281,278,276,277,285,286,287,284,282,283,598,599,597,594,595,596,589,590,588,592,593,591,688,695,701,694,542,541,540,544,545,543,547,548,546,550,551,549,340,341,339,336,337,338,346,347,345,342,343,344,351,352,353,350,348,349,357,358,359,356,354,355,24,25,26,27,28,29,30,31,32,33,34,35,568,569,567,564,565,566,574,575,573,570,571,572,665,672,673,671,248,247,246,250,251,249,245,243,244,241,242,240,253,254,252,256,257,255,259,260,258,262,263,261,58,59,57,54,55,56,49,50,48,52,53,51,387,388,389,386,384,385,393,394,395,392,390,391,66,67,68,69,70,71,64,65,63,60,61,62,666,667,674,668 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 = {64} 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 20:01:42 · history