Equation 677 Database

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Magma be017caaf605…

magma be017caaf605
Size
705
Isomorphism class hash
be017caaf605a11ea81ead7c4964fbb8be29566e8c4baf060651749f2d817ef2
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 15:28:31
Display reorder
660,594,234,596,586,592,554,235,556,546,552,574,236,576,566,572,237,654,656,646,652,238,614,616,606,612,239,634,636,626,632,232,492,496,486,490,233,512,516,506,510,231,534,536,526,532,472,228,476,466,470,428,229,436,434,435,452,230,456,446,450,685,689,694,690,590,78,582,597,591,550,79,542,557,551,570,80,562,577,571,81,650,642,657,651,82,610,602,617,611,83,630,622,637,631,76,488,482,497,489,77,508,502,517,509,75,530,522,537,531,468,72,462,477,469,427,73,437,439,438,448,74,442,457,449,686,691,688,695,117,23,124,136,147,118,21,125,137,148,119,22,123,135,149,19,116,120,132,146,20,114,121,133,144,18,115,122,134,145,14,108,130,142,153,12,109,131,143,154,13,110,129,141,155,111,17,126,138,152,112,15,127,139,150,113,16,128,140,151,675,683,663,679,307,262,278,210,380,308,263,276,211,378,306,261,277,212,379,258,310,281,213,383,259,311,279,214,381,260,309,280,215,382,253,305,284,208,375,254,303,282,209,376,252,304,283,207,377,301,256,287,204,374,302,257,285,205,372,300,255,286,206,373,678,672,676,662,598,88,587,589,583,558,89,547,549,543,578,87,567,569,563,84,658,647,649,643,85,619,607,609,603,86,638,627,629,623,94,498,487,495,483,95,519,507,515,503,93,538,527,529,523,478,90,467,474,463,432,91,426,430,425,458,92,447,455,443,698,697,703,687,599,221,595,581,588,559,219,555,540,548,579,220,575,560,568,217,659,655,641,648,218,618,615,601,608,216,639,635,621,628,227,499,493,480,494,225,518,513,500,514,226,539,535,520,528,479,223,473,461,475,433,224,429,423,431,459,222,453,440,454,701,702,704,696,580,29,584,585,593,541,27,544,545,553,561,28,564,565,573,25,640,644,645,653,26,600,604,605,613,24,620,624,625,633,35,481,484,485,491,33,501,504,505,511,34,521,524,525,533,460,31,464,465,471,424,32,420,421,422,441,30,444,445,451,693,692,700,699,368,71,356,104,332,366,69,354,102,330,367,70,355,103,331,67,371,359,107,335,68,369,357,105,333,66,370,358,106,334,62,363,351,99,327,60,364,352,100,328,61,365,353,101,329,362,65,350,98,326,360,63,348,96,324,361,64,349,97,325,673,666,671,681,320,272,249,296,392,318,270,250,294,390,319,271,251,295,391,275,323,248,299,395,273,321,246,297,393,274,322,247,298,394,267,315,240,291,387,268,316,241,292,388,269,317,242,293,389,314,266,243,290,386,312,264,244,288,384,313,265,245,289,385,661,674,664,668,172,59,184,195,160,173,57,185,196,161,171,58,183,197,159,55,168,180,194,156,56,169,181,192,157,54,170,182,193,158,50,178,190,201,166,48,179,191,202,167,49,177,189,203,165,174,53,186,200,162,175,51,187,198,163,176,52,188,199,164,670,680,667,665,344,9,404,416,40,342,10,402,414,41,343,11,403,415,39,8,347,407,419,36,6,345,405,417,37,7,346,406,418,38,1,339,399,411,46,0,340,400,412,47,2,341,401,413,45,338,3,398,410,42,336,4,396,408,43,337,5,397,409,44,682,684,669,677 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#19ea6a1480a1f5a2ac1b5eeb32448a05ed8c6404ec648162b4da66f77bce13ec, 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 15:28:32 · history