Equation 677 Database

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Magma 14c9452b7945…

magma 14c9452b7945
Size
705
Isomorphism class hash
14c9452b79456ae8b6d4db41d032e7867e4f4600c69c2eeaef7852f5be1fb052
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 15:35:09
Display reorder
666,208,207,209,206,204,205,213,214,215,212,210,211,292,293,291,288,289,290,298,299,297,294,295,296,320,318,319,323,321,322,315,316,317,314,312,313,309,310,311,308,306,307,300,301,302,303,304,305,334,335,333,330,331,332,325,326,324,328,329,327,686,697,700,699,161,160,159,156,157,158,166,167,165,162,163,164,616,617,615,612,613,614,622,623,621,618,619,620,82,83,81,78,79,80,73,74,72,76,77,75,62,60,61,65,63,64,68,66,67,71,69,70,606,607,608,609,610,611,604,605,603,600,601,602,684,696,703,694,135,137,136,133,134,132,143,141,142,139,140,138,275,273,274,271,272,270,266,264,265,269,267,268,249,250,251,248,246,247,240,241,242,243,244,245,277,278,276,280,281,279,283,284,282,286,287,285,656,654,655,659,657,658,651,652,653,650,648,649,661,678,667,673,25,24,26,27,28,29,30,31,32,33,34,35,232,233,231,228,229,230,238,239,237,234,235,236,203,201,202,199,200,198,194,192,193,197,195,196,182,180,181,185,183,184,188,186,187,191,189,190,222,223,224,225,226,227,220,221,219,216,217,218,664,676,669,688,579,581,580,577,578,576,587,585,586,583,584,582,520,521,519,516,517,518,526,527,525,522,523,524,548,546,547,551,549,550,543,544,545,542,540,541,537,538,539,536,534,535,528,529,530,531,532,533,563,561,562,559,560,558,554,552,553,557,555,556,685,698,702,693,359,358,357,354,355,356,349,350,348,352,353,351,395,393,394,391,392,390,386,384,385,389,387,388,419,417,418,415,416,414,410,408,409,413,411,412,398,396,397,401,399,400,404,402,403,407,405,406,383,381,382,379,380,378,374,372,373,377,375,376,682,690,701,692,59,58,57,54,55,56,49,50,48,52,53,51,630,631,632,633,634,635,628,629,627,624,625,626,255,256,257,254,252,253,261,262,263,260,258,259,643,644,642,646,647,645,641,639,640,637,638,636,41,39,40,37,38,36,47,45,46,43,44,42,683,691,704,695,113,112,111,108,109,110,118,119,117,114,115,116,466,467,465,462,463,464,457,458,456,460,461,459,439,440,438,442,443,441,437,435,436,433,434,432,429,430,431,428,426,427,420,421,422,423,424,425,453,454,455,452,450,451,444,445,446,447,448,449,665,679,668,687,122,121,120,124,125,123,127,128,126,130,131,129,595,596,594,598,599,597,593,591,592,589,590,588,106,107,105,102,103,104,97,98,96,100,101,99,86,84,85,89,87,88,92,90,91,95,93,94,1,0,2,3,4,5,6,7,8,9,10,11,662,681,671,672,568,567,569,566,564,565,573,574,575,572,570,571,504,505,506,507,508,509,510,511,512,513,514,515,489,490,491,488,486,487,480,481,482,483,484,485,470,468,469,473,471,472,476,474,475,479,477,478,495,496,497,494,492,493,501,502,503,500,498,499,663,677,670,689,13,12,14,15,16,17,18,19,20,21,22,23,149,147,148,145,146,144,155,153,154,151,152,150,347,345,346,343,344,342,338,336,337,341,339,340,369,370,371,368,366,367,360,361,362,363,364,365,171,172,173,170,168,169,177,178,179,176,174,175,660,680,675,674 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, 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 15:35:10 · history