Equation 677 Database

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Magma db240d2a066a…

magma db240d2a066a
Size
705
Isomorphism class hash
db240d2a066a9c140613ecb0e7f054b824ed7dc38d6f71db2058e8875c63b0b2
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 21:52:33
Display reorder
704,56,18,35,45,54,19,46,33,55,20,47,34,59,21,31,44,57,22,32,42,58,23,43,30,16,51,26,36,17,52,37,24,53,15,38,25,50,12,29,39,13,48,40,27,14,49,41,28,62,63,61,71,70,60,65,66,67,68,69,64,683,680,682,681,207,11,551,192,208,9,193,549,209,10,194,550,206,7,547,195,204,8,548,196,205,6,197,546,2,213,542,198,1,214,199,540,215,0,200,541,212,5,545,201,3,210,202,543,4,211,203,544,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,147,437,120,134,148,435,132,121,149,436,133,122,146,433,123,137,144,434,124,135,145,432,136,125,443,153,126,140,441,154,138,127,155,442,139,128,152,439,129,143,440,150,141,130,438,151,142,131,167,165,166,163,164,162,158,156,160,161,159,157,669,671,668,670,365,99,337,348,363,100,349,338,364,101,350,336,361,98,340,351,362,96,341,352,360,97,353,339,105,371,343,354,106,369,355,344,370,107,356,342,367,104,346,357,102,368,358,347,103,366,359,345,381,382,383,380,378,379,372,373,377,375,376,374,679,676,678,677,523,190,503,515,524,191,513,501,522,189,514,502,526,186,499,511,527,187,500,512,525,188,510,498,181,521,494,506,182,519,504,492,520,180,505,493,517,184,497,509,185,518,507,495,183,516,508,496,533,531,532,529,530,528,539,537,534,535,536,538,689,690,688,691,614,230,638,604,612,228,605,636,613,229,603,637,617,233,641,600,615,231,639,601,616,232,602,640,236,620,644,610,234,618,611,642,619,235,609,643,623,239,647,606,237,621,607,645,238,622,608,646,631,632,630,634,635,633,629,627,624,625,626,628,692,694,693,695,456,176,480,449,457,174,447,481,458,175,448,482,459,179,483,445,460,177,484,446,461,178,444,485,171,462,486,455,172,463,453,487,464,173,454,488,465,170,489,451,168,466,452,490,169,467,450,491,476,474,475,479,477,478,471,472,469,470,468,473,661,662,660,663,245,72,269,281,243,73,279,267,244,74,280,268,241,75,265,277,242,76,266,278,240,77,276,264,78,251,275,287,79,249,285,273,250,80,286,274,247,81,271,283,82,248,284,272,83,246,282,270,261,262,263,260,258,259,252,253,257,255,256,254,685,686,684,687,296,87,319,331,294,88,332,320,295,89,330,318,299,86,322,334,297,84,323,335,298,85,333,321,93,291,317,329,94,292,327,315,293,95,328,316,290,92,313,325,90,288,326,314,91,289,324,312,303,304,305,302,300,301,309,310,307,308,306,311,698,697,699,696,398,114,421,387,396,115,388,422,397,116,389,420,401,117,424,386,399,118,425,384,400,119,385,423,112,404,427,393,113,402,394,428,403,111,395,426,407,108,430,392,109,405,390,431,110,406,391,429,416,414,415,419,417,418,411,412,409,410,408,413,666,665,667,664,593,226,565,577,591,227,578,566,592,225,576,564,589,222,568,580,590,223,569,581,588,224,579,567,217,599,571,583,218,597,584,572,598,216,582,570,595,220,574,586,221,596,587,575,219,594,585,573,560,558,559,563,561,562,555,556,553,554,552,557,674,673,675,672 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#f8838644c69f7fdfa74529bfff2a78ed4214bd0b4502e0a1aafa31f9fac0d26b, 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 21:52:33 · history