Equation 677 Database

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Magma 1336ab846b13…

magma 1336ab846b13
Size
705
Isomorphism class hash
1336ab846b13ff669764133512bf6c51b185f66e4c73630429223979a2cf7647
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 21:47:33
Display reorder
660,121,120,122,123,124,125,126,127,128,129,130,131,133,134,132,136,137,135,139,140,138,142,143,141,153,154,155,152,150,151,144,145,146,147,148,149,166,167,165,162,163,164,157,158,156,160,161,159,87,88,89,86,84,85,93,94,95,92,90,91,694,687,695,703,265,264,266,267,268,269,270,271,272,273,274,275,277,278,276,280,281,279,283,284,282,286,287,285,297,298,299,296,294,295,288,289,290,291,292,293,309,310,311,308,306,307,300,301,302,303,304,305,52,53,51,48,49,50,58,59,57,54,55,56,692,689,698,701,235,234,236,237,238,239,232,233,231,228,229,230,247,248,246,250,251,249,245,243,244,241,242,240,260,258,259,263,261,262,255,256,257,254,252,253,224,222,223,227,225,226,219,220,221,218,216,217,9,10,11,8,6,7,1,0,2,3,4,5,665,662,677,681,519,521,520,517,518,516,527,525,526,523,524,522,481,482,480,484,485,483,487,488,486,490,491,489,502,503,501,498,499,500,493,494,492,496,497,495,513,514,515,512,510,511,504,505,506,507,508,509,63,64,65,62,60,61,69,70,71,68,66,67,668,666,673,683,385,384,386,387,388,389,390,391,392,393,394,395,398,396,397,401,399,400,404,402,403,407,405,406,410,408,409,413,411,412,416,414,415,419,417,418,383,381,382,379,380,378,374,372,373,377,375,376,321,322,323,320,318,319,312,313,314,315,316,317,693,688,696,700,188,187,186,190,191,189,185,183,184,181,182,180,599,597,598,595,596,594,590,588,589,593,591,592,196,197,195,192,193,194,202,203,201,198,199,200,173,171,172,169,170,168,179,177,178,175,176,174,533,531,532,529,530,528,539,537,538,535,536,534,691,685,697,704,613,612,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,649,650,648,652,653,651,655,656,654,658,659,657,609,610,611,608,606,607,600,601,602,603,604,605,690,686,699,702,439,438,440,441,442,443,436,437,435,432,433,434,450,451,452,453,454,455,448,449,447,444,445,446,466,467,465,462,463,464,457,458,456,460,461,459,478,479,477,474,475,476,469,470,468,472,473,471,36,37,38,39,40,41,42,43,44,45,46,47,670,671,672,684,587,586,585,582,583,584,577,578,576,580,581,579,547,548,546,550,551,549,545,543,544,541,542,540,558,559,560,561,562,563,556,557,555,552,553,554,570,571,572,573,574,575,568,569,567,564,565,566,214,215,213,210,211,212,205,206,204,208,209,207,669,661,676,679,29,28,27,24,25,26,34,35,33,30,31,32,107,105,106,103,104,102,98,96,97,101,99,100,113,111,112,109,110,108,119,117,118,115,116,114,73,74,72,76,77,75,79,80,78,82,83,81,22,23,21,18,19,20,13,14,12,16,17,15,667,663,675,682,368,367,366,370,371,369,365,363,364,361,362,360,332,330,331,335,333,334,327,328,329,326,324,325,339,340,341,338,336,337,345,346,347,344,342,343,353,351,352,349,350,348,359,357,358,355,356,354,429,430,431,428,426,427,420,421,422,423,424,425,678,664,674,680 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, 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 21:47:34 · history