Equation 677 Database

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Magma e7df6917d108…

magma e7df6917d108
Size
705
Isomorphism class hash
e7df6917d108eb7d9ed2e89e5f39e2a87bb8c1fd988334622f0a8745fff589c2
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 19:10:25
Display reorder
660,588,595,591,584,183,548,184,555,551,544,575,185,568,571,564,655,648,182,651,644,615,608,180,611,604,181,628,635,631,624,491,495,488,189,484,515,508,190,511,504,535,528,191,531,524,468,475,188,471,464,426,430,186,437,436,448,455,187,451,444,691,702,687,695,590,581,598,599,126,550,127,540,558,559,561,128,570,579,578,640,650,129,659,658,601,610,130,618,619,131,630,620,639,638,498,482,490,124,499,502,510,125,518,519,522,530,123,539,538,470,462,120,478,479,427,422,121,438,439,450,442,122,459,458,690,692,689,700,412,380,115,413,49,409,50,378,116,408,379,48,410,114,411,383,418,52,118,419,381,415,53,119,414,51,416,382,117,417,113,375,403,55,402,376,405,56,111,404,377,406,54,112,407,400,374,58,109,401,396,372,59,110,397,398,373,57,108,399,675,683,684,677,253,246,73,284,157,254,158,247,74,282,248,156,252,72,283,249,256,160,76,287,250,257,161,77,285,159,255,251,75,286,79,244,259,163,279,245,260,164,80,280,243,258,162,78,281,262,240,166,82,278,263,241,167,83,276,261,242,165,81,277,678,663,672,671,586,592,596,593,22,546,23,552,556,553,572,21,566,576,573,652,646,18,656,653,612,606,19,616,613,20,626,632,636,633,496,492,486,13,493,512,506,14,516,513,532,526,12,536,533,466,472,16,476,473,433,435,17,431,428,446,452,15,456,453,696,698,686,694,589,585,594,587,320,549,318,545,554,547,565,319,569,574,567,645,649,323,654,647,605,609,321,614,607,322,629,625,634,627,494,485,489,315,487,505,509,316,514,507,525,529,317,534,527,469,465,314,474,467,434,432,312,429,425,449,445,313,454,447,693,685,688,697,583,582,597,580,174,543,175,542,557,541,562,176,563,577,560,642,643,177,657,641,602,603,178,617,600,179,623,622,637,621,497,480,483,172,481,501,503,173,517,500,521,523,171,537,520,463,461,168,477,460,424,423,169,421,420,443,441,170,457,440,701,703,704,699,84,267,308,42,235,85,236,268,306,43,269,234,86,307,44,266,87,238,311,45,264,88,239,309,46,237,89,265,310,47,303,273,90,233,40,274,91,231,304,41,275,92,232,305,39,93,272,229,302,36,94,270,230,300,37,95,271,228,301,38,666,674,670,665,192,332,63,215,4,193,5,330,64,213,331,3,194,65,214,335,195,1,62,211,333,196,0,60,212,2,197,334,61,210,69,327,198,10,206,328,199,11,70,204,329,200,9,71,205,201,326,6,68,209,202,324,7,66,207,203,325,8,67,208,682,662,680,667,149,392,344,98,141,147,142,390,342,96,391,143,148,343,97,395,145,140,347,101,393,146,138,345,99,139,144,394,346,100,339,387,155,132,104,388,153,133,340,102,389,154,134,341,103,151,386,135,338,107,152,384,136,336,105,150,385,137,337,106,668,681,673,679,224,368,296,356,32,222,30,366,294,354,367,31,223,295,355,371,227,35,299,359,369,225,33,297,357,34,226,370,298,358,291,363,219,27,351,364,220,28,292,352,365,221,29,293,353,218,362,26,290,350,216,360,24,288,348,217,361,25,289,349,664,669,661,676 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#8e5759f62ba231b7a190308c910bac46805bb85b5237b53b53611999ba1c2d7b, 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 19:10:26 · history