Equation 677 Database

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Magma f2d2b4647059…

magma f2d2b4647059
Size
705
Isomorphism class hash
f2d2b46470592a40891c30ca5528da4078f23ac2780466988143533043831cbc
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 20:01:03
Display reorder
665,135,137,136,133,134,132,143,141,142,139,140,138,643,644,642,646,647,645,641,639,640,637,638,636,18,19,20,21,22,23,16,17,15,12,13,14,278,276,277,281,279,280,284,282,283,287,285,286,252,253,254,255,256,257,258,259,260,261,262,263,683,688,692,704,390,392,391,395,393,394,387,388,389,386,384,385,309,310,311,308,306,307,300,301,302,303,304,305,3,4,5,2,1,0,9,10,11,8,6,7,415,416,414,418,419,417,413,411,412,409,410,408,426,427,428,429,430,431,424,425,423,420,421,422,676,685,687,701,205,204,206,207,208,209,210,211,212,213,214,215,240,241,242,243,244,245,246,247,248,249,250,251,83,81,82,79,80,78,74,72,73,77,75,76,360,361,362,363,364,365,366,367,368,369,370,371,346,347,345,342,343,344,337,338,336,340,341,339,660,669,679,694,573,575,574,571,572,570,566,564,565,569,567,568,521,519,520,517,518,516,527,525,526,523,524,522,593,591,592,589,590,588,599,597,598,595,596,594,453,454,455,452,450,451,444,445,446,447,448,449,623,621,622,619,620,618,614,612,613,617,615,616,663,668,673,697,314,313,312,316,317,315,319,320,318,322,323,321,376,377,375,372,373,374,382,383,381,378,379,380,436,437,435,432,433,434,442,443,441,438,439,440,335,333,334,331,332,330,326,324,325,329,327,328,396,397,398,399,400,401,402,403,404,405,406,407,680,686,690,702,49,48,50,51,52,53,54,55,56,57,58,59,163,164,162,166,167,165,161,159,160,157,158,156,176,174,175,179,177,178,171,172,173,170,168,169,187,188,186,190,191,189,185,183,184,181,182,180,199,200,198,202,203,201,197,195,196,193,194,192,674,684,689,703,264,266,265,269,267,268,272,270,271,275,273,274,43,44,42,46,47,45,41,39,40,37,38,36,652,653,651,648,649,650,658,659,657,654,655,656,148,149,147,144,145,146,154,155,153,150,151,152,288,289,290,291,292,293,294,295,296,297,298,299,675,691,699,700,236,235,234,238,239,237,233,231,232,229,230,228,64,65,63,60,61,62,70,71,69,66,67,68,221,219,220,217,218,216,227,225,226,223,224,222,102,103,104,105,106,107,100,101,99,96,97,98,354,355,356,357,358,359,352,353,351,348,349,350,661,671,677,693,626,625,624,628,629,627,631,632,630,634,635,633,605,603,604,601,602,600,611,609,610,607,608,606,117,118,119,116,114,115,108,109,110,111,112,113,125,123,124,121,122,120,131,129,130,127,128,126,580,581,579,576,577,578,586,587,585,582,583,584,664,667,678,698,481,480,482,483,484,485,486,487,488,489,490,491,528,529,530,531,532,533,534,535,536,537,538,539,456,457,458,459,460,461,462,463,464,465,466,467,561,562,563,560,558,559,552,553,554,555,556,557,505,506,504,508,509,507,511,512,510,514,515,513,662,670,681,696,503,502,501,498,499,500,493,494,492,496,497,495,33,34,35,32,30,31,24,25,26,27,28,29,545,543,544,541,542,540,551,549,550,547,548,546,468,469,470,471,472,473,474,475,476,477,478,479,89,87,88,85,86,84,95,93,94,91,92,90,666,682,672,695 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {63} 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 20:01:04 · history