Equation 677 Database

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Magma 38d381e80562…

magma 38d381e80562
Size
705
Isomorphism class hash
38d381e805624cc2a290364dbca23c48bc5d49eefac3b0fbf3e52b4d177dde77
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 20:34:27
Display reorder
660,162,300,57,63,178,58,163,64,179,301,59,302,164,65,177,299,56,165,62,174,297,54,166,60,175,298,55,167,61,176,160,48,306,69,169,161,49,307,70,170,159,50,308,71,168,51,156,305,68,172,52,157,303,66,173,67,53,158,304,171,685,686,688,687,402,103,387,227,208,388,403,225,209,104,389,102,404,226,207,106,390,401,223,204,107,391,399,224,205,105,392,400,222,206,393,385,101,218,214,394,386,99,216,215,395,384,100,217,213,381,396,97,221,210,382,397,98,219,211,220,383,398,96,212,701,702,704,703,559,285,545,580,568,546,560,581,569,286,544,287,561,582,570,288,548,558,583,571,289,549,556,584,572,290,547,557,585,573,565,551,291,586,574,566,552,292,587,575,567,550,293,588,576,554,564,294,589,577,555,562,295,590,578,591,553,563,296,579,670,669,672,671,233,30,427,411,110,428,231,412,108,31,426,32,232,413,109,33,423,229,414,113,34,424,230,415,111,35,425,228,416,112,239,418,28,409,116,237,419,29,410,114,238,417,27,408,115,421,235,24,405,119,422,236,25,406,117,407,420,234,26,118,680,677,679,678,468,244,454,441,429,455,469,442,430,245,453,243,470,443,431,240,457,467,444,432,241,458,465,445,433,242,456,466,446,434,474,460,250,447,435,475,461,251,448,436,476,459,249,449,437,463,473,246,450,438,464,471,247,451,439,452,462,472,248,440,689,690,691,692,495,93,1,268,512,0,496,269,510,94,2,95,497,267,511,92,3,498,264,508,90,4,499,265,509,91,5,500,266,507,493,6,84,274,503,494,7,85,275,501,492,8,86,273,502,9,489,87,270,506,10,490,88,271,504,272,11,491,89,505,697,698,700,699,615,603,651,632,626,649,613,633,627,601,650,602,614,631,625,599,647,611,628,622,600,648,612,629,623,598,646,610,630,624,606,642,594,638,617,604,640,592,639,618,605,641,593,637,616,645,609,597,634,620,643,607,595,635,621,636,644,608,596,619,661,662,664,663,330,39,315,188,81,316,331,186,82,40,317,41,332,187,83,38,318,329,191,80,36,319,327,189,78,37,320,328,190,79,321,313,45,183,72,322,314,46,184,73,323,312,47,185,74,309,324,44,182,75,310,325,42,180,76,181,311,326,43,77,682,681,684,683,525,19,515,283,537,513,526,284,538,20,514,18,524,282,539,22,518,528,279,536,23,516,529,280,534,21,517,527,281,535,658,656,17,657,659,530,519,15,523,543,654,653,16,652,655,522,532,13,277,542,520,533,14,278,540,276,521,531,12,541,693,694,696,695,133,481,123,260,149,124,134,258,147,482,125,480,132,259,148,477,122,136,263,145,478,120,137,261,146,479,121,135,262,144,139,129,487,255,155,140,130,488,256,153,138,131,486,257,154,128,142,483,254,151,126,143,484,252,152,253,127,141,485,150,666,665,668,667,349,202,343,372,367,344,350,373,368,203,342,201,348,374,366,198,339,345,371,363,199,340,346,369,364,200,341,347,370,365,355,334,193,378,358,356,335,194,379,359,354,333,192,380,357,337,351,196,377,361,338,352,197,375,362,376,336,353,195,360,674,673,676,675 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#c633edfa20dc6722982152bc303db7386181f99f3fbdfeb33272ccd5420b69f5, 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 20:34:28 · history