Equation 677 Database

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Magma b002fcbab2fc…

magma b002fcbab2fc
Size
705
Isomorphism class hash
b002fcbab2fcb3815b7b15e834380f217b2b9713c8afa019bfbf769ad27c0438
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 20:04:06
Display reorder
660,33,35,34,31,32,30,41,39,40,37,38,36,530,528,531,529,533,532,534,535,537,536,538,539,525,524,526,527,517,516,518,519,521,520,522,523,555,552,553,554,559,556,557,558,563,560,561,562,548,551,549,550,540,543,541,542,544,547,545,546,682,681,684,683,262,261,263,264,265,266,259,260,258,255,256,257,480,482,481,483,486,487,484,485,490,491,488,489,478,479,477,476,470,471,468,469,474,475,472,473,504,506,507,505,508,510,511,509,513,514,515,512,502,501,503,500,494,492,495,493,498,496,499,497,699,697,700,698,107,106,105,109,110,108,104,102,103,100,101,99,354,355,339,50,357,48,356,340,359,49,358,341,352,53,353,338,349,51,348,336,351,52,350,337,345,366,45,367,346,368,46,369,347,371,47,370,365,344,44,364,360,342,42,361,362,343,43,363,665,668,666,667,398,397,399,400,401,402,403,396,408,419,417,418,404,405,407,406,119,130,115,286,120,131,114,287,68,132,118,284,66,133,116,285,67,134,117,283,279,124,129,125,416,414,415,413,412,409,411,410,123,282,126,112,121,280,127,113,122,281,128,111,688,685,686,687,2,0,1,4,5,3,7,8,6,10,11,9,435,433,434,432,437,436,439,438,440,441,443,442,428,429,431,430,420,421,423,422,424,425,427,426,458,457,456,459,462,460,461,463,466,464,465,467,452,454,453,455,445,446,444,447,448,450,449,451,696,695,693,694,234,236,235,232,233,231,242,240,241,238,239,237,230,206,218,194,204,192,228,216,205,193,229,217,202,190,226,214,203,191,227,215,201,189,225,213,209,197,185,221,207,195,183,219,208,196,184,220,200,212,188,224,198,210,186,222,199,211,187,223,701,702,704,703,145,144,146,143,141,142,135,136,137,138,139,140,625,626,627,624,630,628,629,631,634,633,632,635,622,620,621,623,614,612,613,615,618,616,617,619,651,650,648,649,655,654,652,653,659,658,657,656,646,647,645,644,638,639,636,637,642,643,641,640,661,663,662,664,251,250,249,253,254,252,248,246,247,244,245,243,164,375,151,177,376,178,162,152,377,179,163,150,374,180,160,147,372,181,161,148,373,182,159,149,157,381,175,170,158,382,176,168,156,383,174,169,380,153,171,166,378,154,172,167,379,155,173,165,677,678,680,679,55,54,56,57,58,59,60,61,62,63,64,65,90,387,91,20,388,18,92,88,389,19,87,89,386,23,95,97,384,21,98,94,385,22,93,96,82,393,26,14,83,394,24,12,81,395,25,13,392,85,29,17,390,86,27,15,391,84,28,16,692,691,689,690,76,75,77,78,79,80,73,74,72,69,70,71,578,576,577,579,581,583,582,580,585,587,586,584,572,575,574,573,565,567,566,564,568,571,570,569,601,600,603,602,604,605,607,606,608,609,611,610,597,596,599,598,588,589,591,590,593,592,595,594,675,674,676,673,293,292,291,288,289,290,298,299,297,294,295,296,267,305,319,333,303,334,268,320,304,335,269,318,301,332,270,322,302,330,271,323,300,331,272,321,317,311,324,273,315,309,325,274,316,310,326,275,307,313,327,276,308,314,328,277,306,312,329,278,671,672,670,669 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#b8dd5d8f5072bb4839777555438d548fef97075a280814a177ddbc224cea50a0, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 20:04:07 · history