Equation 677 Database

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Magma ae91563b2f0c…

magma ae91563b2f0c
Size
705
Isomorphism class hash
ae91563b2f0c7202a9a0a6c7f3a56e160701b42eb297ff74c981a8ee998175bd
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 21:55:02
Display reorder
660,537,522,529,89,536,482,87,497,489,496,502,88,517,509,516,455,85,447,451,454,474,86,463,468,473,434,84,423,428,433,643,657,649,95,656,603,617,609,93,616,623,637,629,94,636,577,563,569,91,576,597,583,589,92,596,557,543,549,90,556,685,695,701,699,533,526,525,49,532,486,50,493,485,492,506,48,513,505,512,452,52,443,442,444,470,53,466,465,469,430,51,426,425,429,646,653,645,55,652,606,613,605,56,612,626,633,625,54,632,573,566,565,58,572,593,586,585,59,592,553,546,545,57,552,686,689,703,694,353,78,199,172,10,79,173,351,200,11,80,171,352,198,9,349,168,81,202,6,350,169,82,203,7,348,170,83,201,8,76,359,197,178,0,77,357,195,179,2,75,358,196,177,1,355,72,193,174,4,356,73,194,175,5,354,74,192,176,3,668,672,669,682,27,111,389,122,377,112,120,28,387,375,113,121,29,388,376,26,125,110,385,373,24,123,108,386,374,25,124,109,384,372,117,33,395,128,383,118,34,393,126,381,119,35,394,127,382,32,116,391,131,379,30,114,392,129,380,31,115,390,130,378,674,677,664,680,531,524,523,38,527,484,36,491,483,487,504,37,511,503,507,456,41,449,448,450,478,39,464,460,467,436,40,424,421,427,644,651,640,44,647,604,611,601,42,607,624,631,621,43,627,571,564,560,47,567,591,584,580,45,587,551,544,541,46,547,700,690,697,692,535,530,528,104,539,490,102,495,488,499,510,103,515,508,519,453,107,457,458,459,472,105,476,477,479,432,106,437,438,439,650,655,648,99,659,610,615,608,100,619,630,635,628,101,639,575,570,568,98,579,595,590,588,96,599,555,550,548,97,559,688,696,691,687,520,521,534,22,538,481,23,480,494,498,501,21,500,514,518,440,18,441,445,446,461,19,462,471,475,420,20,422,431,435,642,641,654,13,658,602,600,614,14,618,622,620,634,12,638,561,562,574,16,578,581,582,594,17,598,540,542,554,15,558,704,698,702,693,317,288,401,213,227,289,214,315,399,225,290,215,316,400,226,313,212,291,397,223,314,210,292,398,224,312,211,293,396,222,294,323,407,204,218,295,321,405,205,216,296,322,406,206,217,319,297,403,207,221,320,298,404,208,219,318,299,402,209,220,676,679,663,683,164,251,413,140,184,249,138,162,411,185,250,139,163,412,183,167,143,247,409,180,165,141,248,410,181,166,142,246,408,182,242,159,419,135,190,240,160,417,136,191,241,161,418,137,189,158,245,415,134,186,156,243,416,132,187,157,244,414,133,188,675,681,673,684,341,272,365,69,287,270,70,339,363,285,271,71,340,364,286,337,68,275,361,283,338,66,273,362,284,336,67,274,360,282,267,347,371,60,278,268,345,369,61,276,269,346,370,62,277,343,266,367,63,281,344,264,368,64,279,342,265,366,65,280,678,665,667,671,255,236,329,147,305,234,148,256,327,303,235,149,257,328,304,254,146,239,325,301,252,144,237,326,302,253,145,238,324,300,231,261,335,153,311,232,262,333,154,309,233,263,334,155,310,260,230,331,152,307,258,228,332,150,308,259,229,330,151,306,670,661,662,666 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#fbd23cd98406f165f23d6b41307d902a92b7e2e110ccd89116da4983a4804a48, 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 21:55:03 · history