Equation 677 Database

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Magma 55740b5976e2…

magma 55740b5976e2
Size
705
Isomorphism class hash
55740b5976e28f820bfa67a743ca3520b3c1f5c6f2dcbceee185da28ee1d38f8
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 15:32:46
Display reorder
704,85,61,82,36,86,37,62,83,60,38,84,81,88,64,39,78,89,65,40,79,87,63,41,80,91,73,67,42,92,74,68,43,90,72,66,44,76,94,70,45,77,95,71,46,75,93,69,47,54,55,56,57,58,59,52,53,50,48,49,51,681,683,682,680,586,562,565,34,587,35,563,566,561,33,585,564,582,558,30,568,583,559,31,569,584,560,32,567,577,571,553,25,578,572,554,26,576,570,552,24,574,580,556,28,575,581,557,29,573,579,555,27,648,649,650,651,652,653,654,655,658,656,657,659,702,701,700,703,448,430,434,199,449,200,431,432,429,198,447,433,444,426,202,437,445,427,203,435,446,428,201,436,454,440,421,197,455,438,422,195,453,439,420,196,443,450,424,193,441,451,425,194,442,452,423,192,412,413,411,408,409,410,418,419,416,414,415,417,670,669,668,671,313,338,353,172,314,173,336,351,337,171,312,352,316,341,168,349,317,339,169,350,315,340,170,348,319,359,344,178,320,357,342,179,318,358,343,177,355,322,347,174,356,323,345,175,354,321,346,176,331,332,330,334,335,333,329,327,324,325,326,328,677,679,678,676,539,514,517,96,537,97,515,518,513,98,538,516,535,510,99,520,536,511,100,521,534,512,101,519,530,523,505,102,528,524,506,103,529,522,504,104,526,533,508,105,527,531,509,106,525,532,507,107,544,545,543,540,541,542,550,551,548,546,547,549,691,689,688,690,216,241,214,645,217,646,242,215,240,647,218,213,219,244,644,210,220,245,642,211,221,243,643,212,222,205,247,636,223,206,248,637,224,204,246,638,208,225,250,639,209,226,251,640,207,227,249,641,234,235,236,237,238,239,232,233,230,228,229,231,695,692,693,694,469,492,467,8,470,6,493,465,494,7,468,466,472,495,11,463,473,496,9,464,471,497,10,462,475,458,498,3,476,456,499,4,474,457,500,5,461,478,501,2,459,479,502,1,460,477,503,0,487,488,486,490,491,489,485,483,480,481,482,484,661,662,660,663,266,291,262,118,264,119,292,263,293,117,265,261,269,290,114,258,267,288,115,259,268,289,116,260,272,253,297,109,270,254,298,110,271,252,299,108,256,275,296,112,257,273,294,113,255,274,295,111,276,277,278,279,280,281,282,283,287,285,286,284,687,685,684,686,138,163,125,307,139,308,164,123,162,306,140,124,141,166,310,121,142,167,311,122,143,165,309,120,136,131,161,305,137,129,159,303,135,130,160,304,127,132,157,301,128,133,158,302,126,134,156,300,153,154,155,152,150,151,144,145,149,147,148,146,696,698,699,697,362,384,407,185,360,183,385,405,386,184,361,406,365,387,181,403,363,388,182,404,364,389,180,402,368,398,390,191,366,396,391,189,367,397,392,190,401,371,393,187,399,369,394,188,400,370,395,186,374,372,373,377,375,376,380,378,382,383,381,379,664,666,667,665,616,593,607,15,617,16,591,608,592,17,615,606,612,589,14,610,613,590,12,611,614,588,13,609,622,605,599,21,623,603,597,22,621,604,598,23,601,618,595,20,602,619,596,18,600,620,594,19,625,626,624,628,629,627,631,632,633,634,635,630,672,674,675,673 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#200706f015266953205238906f67170c94edeebe72a54762b43b1258f263dcc8, 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 15:32:47 · history