Equation 677 Database

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Magma e287ae1d9364…

magma e287ae1d9364
Size
705
Isomorphism class hash
e287ae1d936450665bc54d926bbfd6edbaf747b838d58ba79e0dcf0e0565fe6a
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 20:41:45
Display reorder
660,228,221,266,249,257,264,229,250,255,219,265,220,230,251,256,269,231,217,248,253,267,232,218,246,254,268,233,216,247,252,227,234,240,272,263,235,225,241,270,261,236,226,242,271,262,223,237,243,275,259,224,238,244,273,260,274,222,239,245,258,685,686,688,687,417,115,396,381,389,397,418,382,387,116,398,117,419,383,388,399,416,118,380,385,400,414,119,378,386,401,415,120,379,384,113,408,372,402,395,409,114,373,403,393,410,112,374,404,394,109,411,375,405,391,110,412,376,406,392,407,111,413,377,390,701,702,704,703,607,204,592,619,39,590,605,617,37,205,591,206,606,618,38,595,603,207,615,42,593,604,208,616,40,594,602,209,614,41,210,598,610,587,45,596,211,608,588,43,597,212,609,589,44,213,601,613,586,48,214,599,611,584,46,585,215,600,612,47,670,669,672,671,437,142,427,445,5,428,435,446,6,143,426,141,436,444,4,430,433,138,448,0,431,434,139,449,2,429,432,140,447,3,133,443,451,425,11,441,134,452,423,12,442,132,450,424,10,136,439,454,421,7,137,440,455,422,8,420,135,438,453,9,680,677,679,678,31,17,152,462,55,150,32,463,56,18,151,16,33,464,57,155,34,13,465,58,153,35,14,466,59,154,36,15,467,60,23,29,460,147,53,30,24,461,148,54,28,22,459,149,52,19,25,456,146,49,20,26,457,144,50,145,21,27,458,51,689,690,691,692,542,176,533,61,523,531,540,62,524,174,532,175,541,63,522,529,545,179,64,526,530,543,177,65,527,528,544,178,66,525,171,548,67,539,521,546,172,68,537,519,547,173,69,538,520,170,551,70,535,517,168,549,71,536,518,534,169,550,72,516,697,698,700,699,84,96,655,628,643,653,82,626,641,94,654,95,83,627,642,651,80,92,631,639,652,81,93,629,640,650,79,91,630,638,87,75,623,646,634,73,85,624,644,632,74,86,625,645,633,90,78,622,649,637,88,76,620,647,635,648,89,77,621,636,661,662,664,663,299,183,276,309,317,277,297,310,315,184,278,185,298,311,316,279,295,182,308,313,280,296,180,306,314,281,294,181,307,312,189,290,300,282,323,288,190,301,283,321,289,191,302,284,322,188,293,303,285,319,186,291,304,286,320,287,187,292,305,318,682,681,684,683,583,196,572,555,122,570,581,556,123,197,571,195,582,557,124,568,579,192,554,125,569,580,193,552,126,567,578,194,553,127,202,574,561,563,128,573,203,562,1,121,658,201,656,657,659,198,577,560,566,131,199,575,558,564,129,565,200,576,559,130,693,694,696,695,502,160,491,506,468,489,503,504,469,161,490,159,501,505,470,487,498,156,509,471,488,499,157,507,472,486,500,158,508,473,166,493,512,482,474,494,167,510,480,475,492,165,511,481,476,162,496,515,485,477,163,497,513,483,478,484,164,495,514,479,666,665,668,667,335,103,371,347,359,369,333,345,357,104,370,105,334,346,358,367,331,106,343,355,368,332,107,344,356,366,330,108,342,354,101,326,338,362,350,324,102,336,360,348,325,100,337,361,349,97,329,341,365,353,98,327,339,363,351,364,99,328,340,352,674,673,676,675 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#cc21ed90a723dc84f76676d15ec858e33ef625916c28841b110b43408fa38d16, 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 20:41:46 · history