Equation 677 Database

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Magma 46574fb17067…

magma 46574fb17067
Size
705
Isomorphism class hash
46574fb17067cb07672fd52f22342aef7c4448cd4170c230a8e48f4c47b54c50
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 20:03:30
Display reorder
660,613,610,165,608,615,166,633,628,635,630,650,653,167,648,655,164,590,593,588,595,550,162,553,548,555,163,570,573,568,575,156,431,429,427,433,157,453,450,448,455,158,473,470,468,475,493,159,490,488,495,513,160,510,508,515,533,161,530,528,535,685,691,697,688,617,601,97,614,611,98,637,634,631,621,640,657,96,654,651,100,580,597,594,591,541,101,557,554,551,99,560,577,574,571,103,435,424,432,430,104,457,441,454,451,102,477,460,474,471,497,106,480,494,491,517,107,500,514,511,537,105,521,534,531,698,694,703,686,345,417,108,321,369,109,346,322,370,418,419,347,110,323,371,111,416,344,320,368,414,112,342,318,366,113,415,343,319,367,114,336,408,312,360,115,337,409,313,361,116,338,410,314,362,339,117,411,315,363,340,118,412,316,364,341,119,413,317,365,664,671,669,681,245,393,195,79,405,196,243,80,406,394,395,244,197,78,407,194,392,241,82,404,390,192,242,83,402,193,391,240,81,403,201,251,384,77,396,202,249,385,75,397,203,250,386,76,398,247,200,387,73,399,248,198,388,74,400,246,199,389,72,401,673,678,667,675,619,600,33,616,609,34,639,636,629,620,641,659,35,656,649,36,581,599,596,589,540,37,559,556,549,38,561,579,576,569,39,439,423,434,428,45,459,440,456,449,46,479,461,476,469,499,40,481,496,489,519,41,501,516,509,539,42,520,536,529,701,687,690,689,602,612,141,604,603,142,622,624,623,632,652,642,143,644,643,140,592,582,584,583,552,138,542,544,543,139,572,562,564,563,132,438,422,421,420,133,442,452,444,443,134,462,472,464,463,482,135,492,484,483,502,136,512,504,503,522,137,532,524,523,696,695,699,693,606,605,237,618,607,238,626,638,627,625,645,646,239,658,647,236,585,586,598,587,545,234,546,558,547,235,565,566,578,567,228,437,425,436,426,229,446,445,458,447,230,466,465,478,467,486,231,485,498,487,506,232,505,518,507,526,233,525,538,527,704,702,700,692,297,277,210,273,257,211,298,274,255,278,276,299,212,275,256,213,280,296,272,253,281,214,294,270,254,215,279,295,271,252,208,288,283,264,263,209,289,284,265,261,207,290,282,266,262,291,204,286,267,259,292,205,287,268,260,293,206,285,269,258,661,676,663,679,168,381,149,131,190,147,169,129,191,382,383,170,148,130,189,145,380,171,127,186,378,146,172,128,187,144,379,173,126,188,155,174,372,122,181,153,175,373,120,182,154,176,374,121,180,177,151,375,125,184,178,152,376,123,185,179,150,377,124,183,662,683,665,674,64,52,300,87,357,301,65,88,358,53,51,63,302,89,359,303,48,60,86,356,49,304,61,84,354,305,50,62,85,355,306,70,58,93,348,307,71,59,94,349,308,69,57,95,350,66,309,54,92,351,67,310,55,90,352,68,311,56,91,353,668,670,684,682,17,43,4,333,222,5,15,334,223,44,47,16,3,335,224,1,30,13,332,225,31,0,14,330,226,2,32,12,331,227,10,23,25,324,220,11,21,26,325,221,9,22,24,326,219,19,6,28,327,216,20,7,29,328,217,18,8,27,329,218,666,677,672,680 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#b88a5e69f4f2e8155017edd6b5c4ba2f90c1abf217fa4fb1e3b057bac30e1168, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 20:03:31 · history