Equation 677 Database

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Magma 57e6e4db436d…

magma 57e6e4db436d
Size
705
Isomorphism class hash
57e6e4db436d92017c06fbde07f53a5808c71e91fb461473e7a0bd1b15fea407
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 21:48:17
Display reorder
666,591,593,592,589,590,588,599,597,598,595,596,594,31,32,30,34,35,33,29,27,28,25,26,24,585,586,587,584,582,583,576,577,578,579,580,581,562,563,561,558,559,560,553,554,552,556,557,555,571,572,570,574,575,573,569,567,568,565,566,564,674,698,700,699,473,472,471,468,469,470,478,479,477,474,475,476,166,167,165,162,163,164,157,158,156,160,161,159,465,466,467,464,462,463,456,457,458,459,460,461,147,148,149,146,144,145,153,154,155,152,150,151,520,521,519,516,517,518,526,527,525,522,523,524,672,697,701,692,5,4,3,1,0,2,10,11,9,6,7,8,143,141,142,139,140,138,134,132,133,137,135,136,349,350,348,352,353,351,355,356,354,358,359,357,330,331,332,333,334,335,328,329,327,324,325,326,345,346,347,344,342,343,336,337,338,339,340,341,660,671,679,682,277,276,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,271,272,270,274,275,273,269,267,268,265,266,264,46,47,45,42,43,44,37,38,36,40,41,39,257,255,256,253,254,252,263,261,262,259,260,258,664,680,681,687,242,241,240,244,245,243,247,248,246,250,251,249,447,448,449,446,444,445,453,454,455,452,450,451,235,236,234,238,239,237,233,231,232,229,230,228,193,194,192,196,197,195,199,200,198,202,203,201,219,220,221,218,216,217,225,226,227,224,222,223,675,696,702,693,390,392,391,395,393,394,387,388,389,386,384,385,67,68,66,70,71,69,65,63,64,61,62,60,377,375,376,373,374,372,383,381,382,379,380,378,407,405,406,403,404,402,398,396,397,401,399,400,368,366,367,371,369,370,363,364,365,362,360,361,676,691,703,694,505,504,506,507,508,509,510,511,512,513,514,515,90,91,92,93,94,95,88,89,87,84,85,86,499,500,498,502,503,501,497,495,496,493,494,492,104,102,103,107,105,106,99,100,101,98,96,97,483,484,485,482,480,481,489,490,491,488,486,487,673,690,704,695,317,316,315,312,313,314,322,323,321,318,319,320,608,606,607,611,609,610,603,604,605,602,600,601,309,310,311,308,306,307,300,301,302,303,304,305,108,109,110,111,112,113,114,115,116,117,118,119,121,122,120,124,125,123,127,128,126,130,131,129,663,670,667,688,434,433,432,436,437,435,439,440,438,442,443,441,19,20,18,22,23,21,17,15,16,13,14,12,427,428,426,430,431,429,425,423,424,421,422,420,54,55,56,57,58,59,52,53,51,48,49,50,411,412,413,410,408,409,417,418,419,416,414,415,661,683,686,685,625,624,626,627,628,629,630,631,632,633,634,635,73,74,72,76,77,75,79,80,78,82,83,81,619,620,618,622,623,621,617,615,616,613,614,612,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,662,677,668,689,173,172,171,168,169,170,178,179,177,174,175,176,214,215,213,210,211,212,205,206,204,208,209,207,546,547,548,549,550,551,544,545,543,540,541,542,191,189,190,187,188,186,182,180,181,185,183,184,531,532,533,530,528,529,537,538,539,536,534,535,665,669,678,684 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 = {61} 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 21:48:18 · history