Equation 677 Database

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Magma 4a9116b8f533…

magma 4a9116b8f533
Size
705
Isomorphism class hash
4a9116b8f533f08882a5604ae4135666c9c4d8c3a290cedd90c64e5e683fbb02
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 15:11:57
Display reorder
660,496,494,490,300,489,510,516,301,514,509,530,534,536,302,529,470,476,303,474,469,430,433,304,432,428,450,456,305,454,449,610,616,306,614,609,630,636,307,634,629,650,656,308,654,649,590,598,309,596,589,550,558,310,556,549,570,578,311,576,569,689,685,686,703,480,491,487,192,484,507,501,193,511,504,527,531,521,194,524,467,460,195,471,464,437,434,196,439,425,447,440,197,451,444,607,600,198,611,604,627,621,199,631,624,647,641,200,651,644,587,580,201,591,584,547,540,202,551,544,567,560,203,571,564,695,688,690,692,18,411,235,214,121,236,19,215,412,122,234,413,20,213,120,238,21,210,410,124,239,22,211,408,125,237,23,212,409,123,233,16,205,417,127,231,17,206,418,128,232,15,204,419,126,229,12,208,416,130,230,13,209,414,131,228,14,207,415,129,679,682,662,666,48,279,152,93,351,150,49,94,280,352,151,281,50,95,353,155,51,92,278,350,153,52,90,276,348,154,53,91,277,349,147,54,84,285,357,148,55,85,286,358,149,56,86,287,359,146,57,87,284,356,144,58,88,282,354,145,59,89,283,355,672,670,667,681,492,482,483,260,495,503,512,258,502,515,523,522,532,259,535,463,472,263,462,475,424,426,261,423,427,443,452,262,442,455,603,612,255,602,615,623,632,256,622,635,643,652,257,642,655,583,592,254,582,597,543,552,252,542,557,563,572,253,562,577,700,693,704,696,497,498,499,105,485,519,517,106,518,505,539,537,538,107,525,479,478,104,477,465,422,420,102,421,429,459,458,103,457,445,619,617,96,618,605,637,639,97,638,625,659,658,98,657,645,599,595,99,594,585,559,555,100,554,545,579,575,101,574,565,697,687,698,699,486,488,481,299,493,500,506,297,508,513,520,528,526,298,533,461,466,295,468,473,435,436,296,438,431,441,446,294,448,453,601,606,290,608,613,620,626,288,628,633,640,646,289,648,653,581,586,293,588,593,541,546,291,548,553,561,566,292,568,573,691,701,694,702,246,7,339,74,274,340,247,72,8,275,341,6,248,73,273,338,249,77,10,270,336,250,75,11,271,337,251,76,9,272,345,244,80,5,265,346,245,78,3,266,347,243,79,4,264,344,240,83,0,268,342,241,81,2,269,343,242,82,1,267,683,665,668,673,221,327,375,135,113,376,219,136,328,111,377,329,220,137,112,374,217,134,326,109,372,218,132,324,110,373,216,133,325,108,381,227,141,333,119,382,225,142,334,117,383,226,143,335,118,380,223,140,332,115,378,224,138,330,116,379,222,139,331,114,664,669,674,677,177,164,399,183,38,400,178,184,162,36,401,163,179,185,37,398,176,182,167,41,396,174,180,165,39,397,175,181,166,40,405,168,189,159,44,406,169,190,160,42,407,170,191,161,43,404,171,188,158,47,402,172,186,156,45,403,173,187,157,46,678,684,676,680,387,27,315,62,363,316,388,60,28,364,317,29,389,61,365,314,386,65,26,362,312,384,63,24,360,313,385,64,25,361,321,393,68,33,369,322,394,66,34,370,323,395,67,35,371,320,392,71,32,368,318,390,69,30,366,319,391,70,31,367,661,671,663,675 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#0898d182914656a7d8331eed416fb390a2b0882bf44ec0102530c706a89c62d3, 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 15:11:59 · history