Equation 677 Database

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Magma 807701aa4bc4…

magma 807701aa4bc4
Size
705
Isomorphism class hash
807701aa4bc499f8a05b9a3048f8724f83c0321b4d083111a170209fd713d5e5
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 16:43:42
Display reorder
660,551,558,228,556,554,578,571,229,576,574,598,591,230,596,594,231,611,618,616,614,631,232,638,636,634,658,233,656,651,654,518,234,516,511,514,235,538,536,531,534,236,498,496,491,494,429,237,428,424,426,456,238,454,449,452,476,239,474,469,472,691,695,688,700,545,541,112,550,543,561,565,113,570,563,580,585,111,590,583,108,605,601,610,603,625,109,621,630,623,641,110,650,645,643,501,118,510,505,504,119,521,530,525,524,117,481,490,485,484,431,114,434,422,421,440,115,448,445,443,460,116,468,465,463,702,694,685,696,390,57,17,414,314,58,391,15,415,312,59,392,16,416,313,13,393,56,417,317,394,14,54,418,315,55,12,419,395,316,48,23,412,388,320,21,49,413,389,318,22,50,411,387,319,51,19,408,384,323,52,20,409,385,321,53,18,410,386,322,661,681,674,678,215,366,165,191,203,367,213,166,189,201,368,214,167,190,202,164,211,369,187,199,212,162,370,188,200,371,163,186,210,198,364,156,182,206,194,157,365,180,204,192,158,363,181,205,193,360,159,185,209,197,361,160,183,207,195,362,161,184,208,196,675,679,682,670,557,544,126,555,542,564,577,127,575,562,584,597,128,595,582,129,617,604,615,602,637,130,624,635,622,644,131,655,657,642,503,124,515,517,502,125,523,535,537,522,123,483,495,497,482,420,120,427,436,432,444,121,453,455,442,464,122,473,475,462,704,693,698,692,553,540,222,559,546,560,573,223,579,566,581,593,224,599,586,225,613,600,619,606,633,226,620,639,626,640,227,659,653,646,500,220,519,513,506,221,520,539,533,526,219,480,499,493,486,430,216,437,435,433,441,217,457,451,446,461,218,477,471,466,699,701,690,703,552,549,147,547,548,569,572,148,567,568,589,592,149,587,588,146,612,609,607,608,632,144,629,627,628,649,145,647,652,648,509,153,507,512,508,154,529,527,532,528,155,489,487,492,488,438,152,439,425,423,459,150,458,450,447,478,151,479,470,467,697,689,687,686,303,0,102,342,91,2,304,103,343,92,1,305,104,344,90,105,302,4,345,94,300,106,5,346,95,3,107,347,301,93,7,100,340,309,89,101,8,341,310,87,99,6,339,311,88,10,96,336,308,85,11,97,337,306,86,9,98,338,307,84,680,666,671,672,252,378,36,278,244,379,253,37,276,245,380,254,38,277,243,39,255,381,281,240,256,40,382,279,241,383,41,280,257,242,376,42,284,258,250,43,377,282,259,251,44,375,283,260,249,372,45,287,261,246,373,46,285,262,247,374,47,286,263,248,684,662,668,673,354,28,63,174,330,29,355,64,175,331,27,356,65,176,332,62,357,24,177,333,358,60,25,178,334,26,61,179,359,335,34,69,172,352,328,70,35,173,353,329,71,33,171,351,327,30,68,168,348,324,31,66,169,349,325,32,67,170,350,326,665,683,669,676,75,294,143,402,270,295,76,141,403,271,296,77,142,404,272,139,74,297,405,273,72,140,298,406,274,299,138,407,73,275,292,134,400,81,268,132,293,401,82,269,133,291,399,83,267,288,137,396,80,264,289,135,397,78,265,290,136,398,79,266,663,677,667,664 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#3c7860e7d36dbffc79bc7c2d0a8ff0a692ab326401712ae14ddffd4858b8cd98, 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 16:43:44 · history