Equation 677 Database

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Magma cd67bbc91a84…

magma cd67bbc91a84
Size
705
Isomorphism class hash
cd67bbc91a844a92fd7aac68cb6e6dc73a7ccb88d518b920d5f049c7fa89b30e
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 19:11:57
Display reorder
660,347,360,616,351,333,345,617,352,334,361,346,362,618,353,335,363,343,619,350,332,364,344,620,348,330,365,342,621,349,331,622,366,338,357,324,623,367,336,358,325,624,368,337,359,326,369,625,341,356,327,370,626,339,354,328,355,371,627,340,329,687,688,686,685,284,451,248,297,221,282,246,298,219,452,283,450,247,299,220,454,287,251,296,217,455,285,249,294,218,453,286,250,295,216,243,449,279,288,227,244,447,280,289,225,245,448,281,290,226,445,242,278,291,223,446,240,276,292,224,293,444,241,277,222,703,704,701,702,59,155,319,611,44,57,320,612,42,153,58,154,318,610,43,151,55,322,614,47,152,56,323,615,45,150,54,321,613,46,317,146,50,609,39,315,144,48,607,40,316,145,49,608,41,149,313,53,605,38,147,314,51,606,36,604,148,312,52,37,671,672,670,669,467,491,96,473,495,465,97,471,496,489,466,490,98,472,497,487,463,99,469,494,488,464,100,470,492,486,462,101,468,493,102,482,458,479,501,103,480,456,477,502,104,481,457,478,503,485,105,461,475,500,483,106,459,476,498,474,484,107,460,499,679,680,678,677,21,192,110,511,204,22,108,512,205,193,23,194,109,510,206,195,20,113,514,207,196,18,111,515,208,197,19,112,513,209,116,198,12,509,210,114,199,13,507,211,115,200,14,508,212,201,119,15,505,213,202,117,16,506,214,504,203,118,17,215,692,691,690,689,551,575,10,557,537,549,11,555,538,573,550,574,9,556,539,571,547,6,553,536,572,548,7,554,534,570,546,8,552,535,0,566,542,563,528,2,564,540,561,529,1,565,541,562,530,569,4,545,559,531,567,5,543,560,532,558,568,3,544,533,699,700,698,697,164,185,77,179,66,162,75,177,67,183,163,184,76,178,68,181,167,73,175,69,182,165,74,176,70,180,166,72,174,71,83,191,159,170,64,81,189,160,168,65,82,190,161,169,63,187,79,158,173,60,188,80,156,171,61,172,186,78,157,62,663,664,662,661,388,409,630,399,376,389,628,400,377,410,387,408,629,401,375,412,384,633,398,372,413,385,631,396,373,411,386,632,397,374,636,415,394,405,382,634,416,395,406,383,635,414,393,407,381,418,639,390,404,378,419,637,391,402,379,403,417,638,392,380,682,683,684,681,652,653,301,655,654,657,302,659,658,656,648,649,300,651,650,596,582,304,597,595,640,641,305,642,643,645,646,303,647,644,307,588,577,602,590,308,586,578,603,591,306,587,576,601,589,584,310,580,598,593,585,311,581,599,594,600,583,309,579,592,695,696,693,694,122,92,35,132,522,120,33,133,523,90,121,91,34,134,524,95,125,31,135,525,93,123,32,136,526,94,124,30,137,527,26,87,128,138,520,24,88,126,139,521,25,89,127,140,519,86,29,131,141,516,84,27,129,142,517,143,85,28,130,518,667,668,665,666,428,252,239,443,266,426,237,441,264,253,427,254,238,442,265,255,431,235,439,269,256,429,236,440,267,257,430,234,438,268,230,258,423,434,272,228,259,424,432,270,229,260,425,433,271,261,233,422,437,275,262,231,420,435,273,436,263,232,421,274,675,676,673,674 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#9017e525a3aedea68e654a603b277c6c50731afc33f3d9497441ab6abb8d2314, 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 19:11:58 · history