Equation 677 Database

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Magma d86b74d564ab…

magma d86b74d564ab
Size
705
Isomorphism class hash
d86b74d564abdf2cac66b9481f470221ef4717e8f5d42e60261b379784803d23
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 19:09:35
Display reorder
660,486,488,491,485,111,506,112,508,511,505,528,113,526,531,525,110,466,468,471,465,108,429,430,431,428,109,446,448,451,445,611,608,606,117,605,628,626,118,631,625,648,646,119,651,645,586,588,116,591,585,546,548,114,551,545,566,568,115,571,565,691,694,690,693,487,484,481,489,20,507,18,504,501,509,524,19,527,521,529,23,467,464,460,469,21,438,437,434,424,22,447,444,440,449,600,604,607,15,609,624,627,16,621,629,644,647,17,641,649,587,584,14,580,589,547,544,12,540,549,567,564,13,560,569,686,688,692,685,327,339,375,312,33,328,34,340,376,313,341,35,329,377,314,32,326,338,374,315,30,324,336,372,316,31,325,337,373,317,381,345,333,24,318,346,334,25,382,319,347,335,26,383,320,332,344,27,380,321,330,342,28,378,322,331,343,29,379,323,675,661,665,669,222,8,144,132,168,223,169,6,145,133,7,170,224,146,134,171,225,11,147,135,172,226,9,148,136,173,227,10,149,137,150,3,220,174,138,4,221,175,151,139,5,219,176,152,140,216,2,177,153,141,217,1,178,154,142,218,0,179,155,143,664,680,663,676,480,494,490,496,68,500,66,514,510,516,534,67,520,530,536,71,461,474,470,476,69,423,426,425,427,70,441,454,450,456,610,614,601,63,616,634,620,64,630,636,654,640,65,650,656,581,594,62,590,598,541,554,60,550,558,561,574,61,570,578,695,689,700,698,497,499,498,493,40,517,41,519,518,513,539,39,538,537,533,36,478,479,477,473,37,420,422,421,432,38,458,459,457,453,618,619,617,46,613,637,639,47,638,633,659,658,45,657,653,597,599,42,596,593,557,559,43,556,553,577,579,44,576,573,702,697,701,699,492,483,482,495,156,512,157,503,502,515,523,158,532,522,535,159,472,463,462,475,160,439,436,435,433,161,452,443,442,455,602,603,612,162,615,623,632,163,622,635,643,652,164,642,655,592,583,165,582,595,552,543,166,542,555,572,563,167,562,575,704,696,687,703,180,207,403,193,51,181,52,208,405,194,209,53,182,406,192,50,183,206,400,196,48,184,204,397,197,49,185,205,399,195,415,213,186,57,199,214,187,58,417,200,215,188,59,418,198,189,212,56,412,202,190,210,54,409,203,191,211,55,410,201,682,683,668,670,302,293,243,234,259,300,260,291,244,235,292,258,301,245,236,262,305,289,242,237,263,303,290,240,238,261,304,288,241,239,249,299,308,257,232,297,306,255,250,233,298,307,256,251,231,311,295,253,248,228,309,296,254,246,229,310,294,252,247,230,662,667,684,673,363,387,101,276,128,364,126,388,99,277,389,127,365,100,278,131,362,386,97,279,129,360,384,98,280,130,361,385,96,281,107,393,369,123,282,394,370,124,105,283,395,371,125,106,284,368,392,122,103,285,366,390,120,104,286,367,391,121,102,287,674,679,672,678,351,402,85,72,271,352,272,404,86,73,407,270,353,84,74,274,350,401,88,75,275,348,396,89,76,273,349,398,87,77,91,414,357,269,78,416,358,267,92,79,419,359,268,90,80,356,413,265,94,81,354,408,266,95,82,355,411,264,93,83,666,677,671,681 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#8cce333a947232ca69e33881346ef6b490f8a5c022184a0ee2c46fc59b5e71a5, 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 19:09:36 · history