Equation 677 Database

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Magma 1a28bb431de2…

magma 1a28bb431de2
Size
705
Isomorphism class hash
1a28bb431de2e0d37afa30e18f78c828955a778b373a50f3f6a29ceb53ec6b72
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 15:14:23
Display reorder
660,563,106,595,573,607,564,107,593,574,605,105,572,565,594,606,562,109,591,576,603,560,110,592,577,604,561,108,590,575,602,112,569,586,579,598,113,570,584,580,596,111,571,585,578,597,115,568,589,582,601,116,566,587,583,599,114,567,588,581,600,687,688,686,685,431,85,407,396,420,429,86,405,397,421,84,398,430,406,422,434,81,410,395,419,432,82,408,393,417,433,83,409,394,418,91,437,413,402,426,92,435,411,403,427,90,436,412,404,428,87,440,416,401,425,88,438,414,399,423,89,439,415,400,424,703,704,701,702,558,186,533,518,537,559,187,534,519,538,185,520,557,535,536,554,182,532,521,540,555,183,530,522,541,556,184,531,523,539,177,549,524,516,543,178,550,525,517,544,176,548,526,515,542,180,552,527,512,546,181,553,528,513,547,179,551,529,514,545,671,672,670,669,226,310,449,239,221,224,311,447,240,222,309,241,225,448,223,229,313,452,238,220,227,314,450,236,218,228,312,451,237,219,316,232,444,245,212,317,230,445,246,213,315,231,446,247,214,319,235,443,244,215,320,233,441,242,216,318,234,442,243,217,679,680,678,677,259,23,94,460,328,257,21,95,461,329,22,459,258,93,327,255,19,97,463,331,256,20,98,464,332,254,18,96,462,330,14,250,100,458,326,12,248,101,456,324,13,249,99,457,325,17,253,103,454,322,15,251,104,455,323,16,252,102,453,321,692,691,690,689,289,497,361,353,282,287,495,362,351,283,496,352,288,360,281,285,500,357,356,278,286,498,358,354,279,284,499,359,355,280,492,295,367,348,273,493,293,368,349,274,494,294,366,350,272,491,291,363,347,276,489,292,364,345,277,490,290,365,346,275,699,700,698,697,130,195,156,151,121,131,196,157,152,122,194,150,129,158,120,133,198,155,147,117,134,199,153,148,118,132,197,154,149,119,193,136,162,142,127,191,137,163,143,128,192,135,164,141,126,189,139,161,145,123,190,140,159,146,124,188,138,160,144,125,663,664,662,661,646,370,622,611,635,644,371,620,612,636,369,613,645,621,637,649,373,625,610,634,647,374,623,608,632,648,372,624,609,633,376,652,628,617,641,377,650,626,618,642,375,651,627,619,643,379,655,631,616,640,380,653,629,614,638,378,654,630,615,639,682,683,684,681,303,200,508,32,167,304,201,509,30,168,202,31,302,507,169,306,203,511,308,166,656,204,658,657,659,305,205,510,307,165,206,301,506,27,173,207,299,504,28,174,208,300,505,29,175,209,297,502,26,172,210,298,503,24,170,211,296,501,25,171,695,696,693,694,482,267,1,337,473,480,268,0,338,471,266,336,481,2,472,478,270,3,333,476,479,271,4,334,474,477,269,5,335,475,265,488,6,343,468,263,486,7,344,469,264,487,8,342,470,261,484,9,339,467,262,485,10,340,465,260,483,11,341,466,667,668,665,666,61,389,39,69,55,62,387,40,70,56,388,71,60,41,54,57,392,42,72,51,58,390,43,73,52,59,391,44,74,53,384,67,37,75,46,385,68,38,76,47,386,66,36,77,45,383,63,33,78,49,381,64,34,79,50,382,65,35,80,48,675,676,673,674 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#0d8cdfdeb3c53efefcd572d9bf5ad220efd26f91f8a2b4cfd66b53f1dccf6eeb, 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 15:14:26 · history