Equation 677 Database

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Magma 4623b3d3783c…

magma 4623b3d3783c
Size
705
Isomorphism class hash
4623b3d3783c5e7eebb6ec0322b8454f71cc3d9a93e169c3bfc384d44959421c
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 15:09:23
Display reorder
660,514,23,516,506,505,534,21,536,526,525,494,22,496,486,485,434,19,436,421,426,20,452,453,449,448,474,18,476,466,465,634,14,636,626,625,654,12,656,646,645,614,13,616,606,605,17,556,558,546,545,15,576,578,566,565,16,596,598,586,585,692,687,690,703,504,165,509,507,502,524,166,529,527,522,484,167,489,487,482,425,164,429,427,423,162,455,457,456,444,464,163,469,467,462,624,156,629,627,622,644,157,649,647,642,604,158,609,607,602,159,544,551,549,542,160,564,571,569,562,161,584,591,589,582,685,702,691,698,364,113,189,197,388,365,111,190,195,389,363,112,191,196,387,360,109,188,193,384,110,361,186,194,385,362,108,187,192,386,370,119,180,203,394,371,117,181,201,395,369,118,182,202,393,115,366,183,199,390,116,367,184,200,391,114,368,185,198,392,662,670,668,677,6,82,56,247,105,7,83,54,248,106,8,81,55,246,107,9,78,59,250,104,79,10,57,251,102,11,80,58,249,103,4,73,51,245,96,5,74,52,243,97,3,72,53,244,98,76,1,50,241,99,77,0,48,242,100,75,2,49,240,101,673,671,680,683,508,277,501,503,515,528,278,521,523,535,488,276,481,483,495,428,280,420,424,435,281,446,443,445,447,468,279,461,463,475,628,283,621,623,635,648,284,640,643,655,608,282,601,603,615,286,550,540,543,557,287,570,560,563,577,285,590,581,583,597,688,701,704,695,519,90,517,518,512,539,91,537,538,532,499,92,497,498,492,439,93,437,438,432,94,442,440,441,450,479,95,478,477,472,639,88,638,637,632,657,89,658,659,652,619,87,618,617,612,84,559,547,548,554,85,579,567,568,574,86,599,587,588,594,693,699,697,686,511,28,500,510,513,531,29,520,530,533,491,27,480,490,493,431,24,422,430,433,25,459,454,458,451,471,26,460,470,473,631,34,620,630,633,651,35,641,650,653,611,33,600,610,613,30,553,541,552,555,31,573,561,572,575,32,593,580,592,595,696,689,694,700,170,260,294,304,352,168,258,295,305,353,169,259,296,303,351,173,263,297,300,348,261,171,298,301,349,172,262,299,302,350,176,255,292,310,358,174,256,293,311,359,175,257,291,309,357,254,179,288,306,354,252,177,289,307,355,253,178,290,308,356,661,666,676,681,412,230,127,328,204,413,228,128,329,205,411,229,126,327,206,408,233,130,324,207,231,409,131,325,208,410,232,129,326,209,418,236,125,334,210,419,234,123,335,211,417,235,124,333,212,239,414,121,330,213,237,415,122,331,214,238,416,120,332,215,664,675,684,679,400,149,376,340,61,401,147,377,341,62,399,148,375,339,60,396,145,372,336,64,146,397,373,337,65,398,144,374,338,63,406,155,382,346,67,407,153,383,347,68,405,154,381,345,66,151,402,378,342,70,152,403,379,343,71,150,404,380,344,69,665,682,678,669,316,275,41,224,140,317,273,39,222,138,315,274,40,223,139,312,271,37,227,143,272,313,38,225,141,314,270,36,226,142,322,266,47,219,135,323,264,45,220,136,321,265,46,221,137,269,318,43,218,134,267,319,44,216,132,268,320,42,217,133,674,672,663,667 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#05c0aaa7a3560fa146ae1951a40d178d675f2688aa4f7579703e2b967da3180b, 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 15:09:25 · history