Equation 677 Database

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Magma 3bac75bd805c…

magma 3bac75bd805c
Size
705
Isomorphism class hash
3bac75bd805cdf8b1be902a585d48eb133a6209db8073995d6402f2cbda369dd
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 18:14:45
Display reorder
660,47,612,617,600,614,45,637,620,634,632,46,652,657,640,654,597,43,592,581,594,44,557,552,540,554,42,577,572,560,574,424,38,435,431,433,36,457,452,441,454,37,477,472,461,474,497,41,492,480,494,517,39,512,500,514,537,40,532,520,534,694,704,692,700,7,613,618,611,608,8,638,631,628,633,6,653,658,651,648,598,10,593,591,588,11,558,553,551,548,9,578,573,571,568,430,5,436,432,427,3,458,453,451,448,4,478,473,471,468,498,0,493,491,488,518,2,513,511,508,538,1,533,531,528,699,691,693,701,50,405,261,333,297,48,262,334,298,406,49,407,263,335,299,260,53,404,332,296,51,258,402,330,294,52,259,403,331,295,324,56,252,396,288,54,253,397,325,289,55,254,398,326,290,255,59,399,327,291,256,57,400,328,292,257,58,401,329,293,669,672,683,666,89,381,141,357,225,87,142,358,226,382,88,383,143,359,227,140,85,380,356,224,86,138,378,354,222,84,139,379,355,223,348,95,132,372,216,93,133,373,349,217,94,134,374,350,218,135,91,375,351,219,136,92,376,352,220,137,90,377,353,221,663,676,678,662,198,601,609,619,607,199,629,639,627,621,200,641,649,659,647,589,201,580,599,587,202,549,541,559,547,203,569,561,579,567,439,196,428,423,426,197,449,440,459,447,195,469,460,479,467,489,192,481,499,487,509,193,501,519,507,529,194,521,539,527,686,702,688,689,60,616,605,604,606,61,625,624,626,636,62,656,645,644,646,585,63,596,584,586,64,545,556,544,546,65,565,576,564,566,438,66,420,422,421,67,445,456,444,446,68,465,476,464,466,485,69,496,484,486,505,70,516,504,506,525,71,536,524,526,695,696,698,703,155,603,615,602,610,153,635,622,630,623,154,643,655,642,650,595,151,583,582,590,152,555,543,542,550,150,575,563,562,570,437,146,434,425,429,144,455,443,442,450,145,475,463,462,470,495,149,483,482,490,515,147,503,502,510,535,148,523,522,530,690,687,685,697,30,273,417,309,213,31,418,310,214,274,32,275,419,311,215,416,33,272,308,212,34,414,270,306,210,35,415,271,307,211,300,28,408,264,204,29,409,265,301,205,27,410,266,302,206,411,24,267,303,207,412,25,268,304,208,413,26,269,305,209,661,670,667,684,15,369,237,321,393,16,238,322,394,370,17,371,239,323,395,236,14,368,320,392,12,234,366,318,390,13,235,367,319,391,312,21,228,360,384,22,229,361,313,385,23,230,362,314,386,231,20,363,315,387,232,18,364,316,388,233,19,365,317,389,679,671,677,664,131,103,249,285,345,129,250,286,346,104,130,102,251,287,347,248,127,106,284,344,128,246,107,282,342,126,247,105,283,343,276,122,240,101,336,120,241,99,277,337,121,242,100,278,338,243,125,97,279,339,244,123,98,280,340,245,124,96,281,341,674,668,682,665,72,179,182,112,162,73,180,113,163,177,74,178,181,111,164,185,75,175,108,165,76,183,176,109,166,77,184,174,110,167,118,78,188,170,160,79,186,168,119,161,80,187,169,117,159,191,81,173,114,156,189,82,171,115,157,190,83,172,116,158,681,680,673,675 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#6f4d58a1f1a96be51a4fbe5ecc6c97c30dc38acf270b654112619a91916a19da, 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 18:14:46 · history