Equation 677 Database

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Magma f291b0db22bd…

magma f291b0db22bd
Size
705
Isomorphism class hash
f291b0db22bd18f635b5f9eb13acc73bca9ddd7da796504e4223a33fb8f60dde
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 20:06:28
Display reorder
660,172,335,103,177,324,173,325,333,104,178,171,326,334,102,179,331,175,327,99,180,332,176,328,100,181,330,174,329,101,182,170,322,341,94,183,323,339,95,168,184,340,321,93,169,185,318,337,97,166,186,319,338,98,167,187,320,336,96,165,188,685,686,688,687,376,84,155,148,79,377,80,85,153,149,375,78,86,154,147,83,372,75,158,151,81,373,76,156,152,82,374,77,157,150,367,70,90,161,146,71,91,159,368,144,92,69,160,366,145,73,89,164,370,142,74,87,162,371,143,72,88,163,369,141,701,702,704,703,308,589,556,551,570,306,568,590,557,552,307,569,591,558,550,588,311,573,559,554,586,309,571,560,555,587,310,572,561,553,314,576,580,562,549,574,581,563,312,547,582,575,564,313,548,579,583,565,317,545,577,584,566,315,546,578,585,567,316,544,670,669,672,671,30,384,403,393,423,31,424,385,404,394,32,425,386,402,395,387,29,422,406,392,388,27,420,407,390,389,28,421,405,391,21,414,382,409,399,415,383,410,22,400,381,416,408,23,401,417,378,412,24,398,418,379,413,25,396,419,380,411,26,397,680,677,679,678,219,471,441,430,452,220,450,472,442,431,221,451,473,443,429,470,222,455,440,426,468,223,453,438,427,469,224,454,439,428,217,458,462,447,436,456,463,448,218,437,464,457,449,216,435,461,465,446,213,432,459,466,444,214,433,460,467,445,215,434,689,690,691,692,527,277,250,244,271,525,272,278,251,245,526,270,276,249,243,273,523,267,253,247,274,524,268,254,248,275,522,269,252,246,533,262,283,256,242,263,284,257,531,240,282,261,255,532,241,265,279,259,529,238,266,280,260,530,239,264,281,258,528,237,697,698,700,699,602,619,651,630,608,603,609,620,649,628,601,607,621,650,629,618,598,604,647,633,616,599,605,648,631,617,600,606,646,632,593,614,625,642,636,615,626,640,594,634,627,613,641,592,635,610,624,645,596,639,611,622,643,597,637,612,623,644,595,638,661,662,664,663,198,119,42,350,112,199,113,117,43,348,200,111,118,44,349,122,197,115,41,353,120,195,116,39,351,121,196,114,40,352,189,110,125,33,345,108,123,34,190,346,124,109,35,191,347,106,128,36,192,344,107,126,37,193,342,105,127,38,194,343,682,681,684,683,210,290,540,297,5,211,3,291,538,295,212,4,289,539,296,293,209,8,543,300,294,207,6,541,298,292,208,7,542,299,201,657,658,659,656,305,285,537,202,301,653,652,654,203,655,2,287,536,204,304,1,288,534,205,302,0,286,535,206,303,693,694,696,695,228,512,490,478,501,229,502,510,491,479,230,503,511,489,477,515,227,500,486,474,513,225,498,487,475,514,226,499,488,476,234,507,518,496,484,508,516,497,235,485,517,509,495,236,483,506,521,492,233,480,504,519,493,231,481,505,520,494,232,482,666,665,668,667,363,16,56,136,66,364,67,17,54,137,365,68,15,55,135,19,362,65,52,139,20,360,63,53,140,18,361,64,51,138,354,57,14,47,134,58,12,45,355,132,13,59,46,356,133,60,10,50,357,130,61,11,48,358,131,62,9,49,359,129,674,673,676,675 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#b9c83ee29c9828886a1d9280722af908f3a23a39dfe3e8d4571f7572270a5310, 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 20:06:29 · history