Equation 677 Database

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Magma 65cfac723687…

magma 65cfac723687
Size
705
Isomorphism class hash
65cfac72368729443cafb40bd659af7c1878891043288011f8e65a2c5ee6b7f2
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 17:27:34
Display reorder
660,55,454,452,450,453,56,474,472,470,473,424,54,432,433,434,514,58,512,510,513,534,59,532,530,533,494,57,492,490,493,53,577,575,573,576,51,597,595,593,596,52,557,555,553,556,633,637,49,635,636,657,50,655,653,656,617,48,615,613,616,691,700,697,694,3,442,446,448,447,4,462,466,468,467,422,5,430,429,426,502,2,506,508,507,522,1,526,528,527,482,0,486,488,487,9,563,567,571,569,10,583,587,591,589,11,543,547,551,549,631,623,8,627,629,643,6,647,651,649,603,7,607,611,609,696,703,686,685,75,398,385,136,160,76,400,386,137,161,384,77,135,159,396,404,74,388,132,156,406,72,389,133,157,402,73,387,134,158,81,411,391,142,166,82,413,392,143,167,83,409,390,141,165,138,417,80,394,162,419,78,395,139,163,415,79,393,140,164,679,681,675,666,205,189,361,301,399,206,190,362,302,401,360,204,300,397,191,188,208,364,304,405,186,209,365,305,407,187,207,363,303,403,211,180,367,307,410,212,181,368,308,412,210,182,366,306,408,310,183,214,370,416,184,215,371,311,418,185,213,369,309,414,672,676,682,663,149,456,449,457,458,147,476,469,477,478,431,148,437,438,436,517,145,509,516,518,538,146,529,537,539,497,144,489,496,498,155,560,572,568,570,153,580,592,588,590,154,541,552,548,550,628,621,151,632,630,640,152,652,648,650,601,150,612,608,610,701,692,689,699,41,445,459,441,455,39,465,479,461,475,439,40,425,435,428,505,37,519,501,515,525,38,536,520,535,485,36,499,481,495,47,566,579,562,578,45,586,599,582,598,46,546,559,542,558,622,626,43,639,638,646,44,659,642,658,606,42,619,602,618,704,687,702,693,18,451,443,444,440,19,471,463,464,460,427,20,421,420,423,511,21,503,504,500,531,22,523,524,521,491,23,483,484,480,16,574,564,565,561,17,594,584,585,581,15,554,544,545,540,625,634,12,624,620,654,13,644,645,641,614,14,604,605,600,698,695,688,690,198,93,313,373,106,199,94,314,374,107,312,200,372,105,95,92,201,316,376,102,90,202,317,377,103,91,203,315,375,104,196,84,319,379,97,197,85,320,380,98,195,86,318,378,96,382,87,192,322,100,88,193,323,383,101,89,194,321,381,99,668,684,678,673,63,171,24,337,349,64,172,25,338,350,26,65,336,348,173,170,62,27,340,352,168,60,28,341,353,169,61,29,339,351,69,177,30,343,355,70,178,31,344,356,71,179,32,342,354,346,176,68,33,358,174,66,34,347,359,175,67,35,345,357,667,662,671,670,217,289,123,282,325,218,290,124,283,326,125,216,284,324,288,292,220,122,285,328,293,221,120,286,329,291,219,121,287,327,223,295,129,280,331,224,296,130,281,332,222,294,131,279,330,276,298,226,128,334,299,227,126,277,335,297,225,127,278,333,677,661,669,683,112,262,238,250,275,113,263,239,251,273,237,111,249,274,261,258,108,234,246,271,259,109,235,247,272,260,110,236,248,270,118,253,229,241,266,119,254,230,242,264,117,252,228,240,265,244,256,114,232,269,257,115,233,245,267,255,116,231,243,268,665,674,680,664 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#5779f8cee5daac7ffda88b67b379fba3aadfa70634d24364b86a2ac7cf85bc20, 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 17:27:35 · history