Equation 677 Database

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Magma af07ea096db9…

magma af07ea096db9
Size
705
Isomorphism class hash
af07ea096db9a4f529df92f224e5d8b3684fcdbbb5a7c4e61908d7f994d10e82
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 21:52:44
Display reorder
704,462,438,488,453,463,439,454,486,464,440,455,487,465,441,491,452,466,442,489,450,467,443,451,490,436,460,483,444,437,461,445,484,459,435,446,485,456,432,482,447,433,457,448,480,434,458,449,481,472,473,471,468,469,470,478,479,476,474,475,477,701,702,700,703,656,658,657,659,649,648,650,651,654,652,655,653,642,640,641,643,646,644,645,647,638,636,639,637,621,620,622,623,613,612,615,614,616,617,619,618,633,632,634,635,625,624,627,626,629,628,631,630,72,73,74,75,76,77,78,79,83,81,82,80,689,690,688,691,288,213,267,280,289,214,281,268,290,215,279,269,291,212,266,276,292,210,264,277,293,211,278,265,204,294,273,286,205,295,287,274,296,206,285,275,297,207,272,282,208,298,283,270,209,299,284,271,308,306,307,311,309,310,303,304,301,302,300,305,674,673,675,672,375,10,400,411,376,11,412,401,377,9,413,399,374,6,396,410,372,7,397,408,373,8,409,398,0,381,406,417,2,382,418,407,383,1,419,405,380,4,402,416,5,378,414,403,3,379,415,404,395,393,394,391,392,390,386,384,388,389,387,385,683,680,682,681,157,89,182,149,158,87,147,180,156,88,148,181,160,85,185,145,161,86,183,146,159,84,144,184,95,163,188,155,93,164,153,186,162,94,154,187,166,91,191,151,92,167,152,189,90,165,150,190,174,175,176,177,178,179,172,173,170,168,169,171,692,694,695,693,360,429,339,351,361,430,352,340,362,431,353,341,363,428,338,350,364,426,336,348,365,427,349,337,420,366,345,357,421,367,358,346,368,422,359,347,369,423,344,356,424,370,354,342,425,371,355,343,334,335,333,330,331,332,325,326,327,328,329,324,697,699,696,698,523,500,547,558,524,498,559,548,522,499,560,546,526,503,550,561,527,501,551,562,525,502,563,549,495,521,545,556,496,519,557,543,520,497,555,544,517,494,541,552,492,518,553,542,493,516,554,540,531,532,533,530,528,529,537,538,535,536,534,539,685,687,686,684,128,199,106,119,126,200,117,107,127,198,118,105,131,202,102,115,129,203,103,116,130,201,114,104,197,123,97,110,195,124,108,98,125,196,109,96,122,193,100,113,194,120,111,101,192,121,112,99,135,136,137,134,132,133,141,142,139,140,138,143,663,660,662,661,239,312,262,222,237,313,223,263,238,314,224,261,235,315,258,225,236,316,259,226,234,317,227,260,318,230,253,220,319,228,221,254,229,320,219,252,233,321,256,216,322,231,217,257,323,232,218,255,241,242,240,244,245,243,247,248,249,250,251,246,678,677,679,676,31,23,56,68,32,21,66,54,30,22,67,55,34,19,59,71,35,20,57,69,33,18,70,58,14,29,51,63,12,27,64,52,28,13,65,53,25,17,50,62,15,26,60,48,16,24,61,49,40,41,39,36,37,38,46,47,44,42,43,45,667,664,666,665,581,512,603,566,579,510,564,604,580,511,565,605,577,515,602,569,578,513,600,567,576,514,568,601,507,587,609,572,508,585,570,610,586,509,571,611,583,506,608,575,504,584,573,606,505,582,574,607,597,598,599,596,594,595,588,589,593,591,592,590,671,669,668,670 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#f8838644c69f7fdfa74529bfff2a78ed4214bd0b4502e0a1aafa31f9fac0d26b, 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 21:52:45 · history