Equation 677 Database

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Magma dcca861c7e4b…

magma dcca861c7e4b
Size
705
Isomorphism class hash
dcca861c7e4bc63c578891db2cca1780047514f47b13bdcb6c4bbd1cb2b4fb68
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 20:47:21
Display reorder
660,567,336,555,590,577,565,337,553,591,578,566,335,554,589,579,332,563,551,586,576,333,564,552,587,574,334,562,550,588,575,546,558,342,581,568,544,556,343,582,569,545,557,341,580,570,561,549,338,584,571,559,547,339,585,572,560,548,340,583,573,687,688,686,685,369,20,406,392,380,370,18,404,393,381,368,19,405,394,382,23,372,409,395,383,21,373,407,396,384,22,371,408,397,385,412,375,15,398,386,410,376,16,399,387,411,374,17,400,388,378,415,14,401,389,379,413,12,402,390,377,414,13,403,391,703,704,701,702,543,175,522,508,496,541,173,520,509,497,542,174,521,510,498,171,539,525,511,499,172,540,523,512,500,170,538,524,513,501,528,534,166,514,502,526,532,164,515,503,527,533,165,516,504,537,531,169,517,505,535,529,167,518,506,536,530,168,519,507,671,672,670,669,249,422,240,230,261,250,423,241,231,262,248,424,239,232,260,425,252,236,233,264,426,253,237,234,265,427,251,238,235,263,246,255,420,228,267,247,256,421,229,268,245,254,419,227,266,258,242,416,224,270,259,243,417,225,271,257,244,418,226,269,679,680,678,677,289,432,279,6,299,287,433,280,7,300,288,431,278,8,301,428,285,282,9,298,429,286,283,10,296,430,284,281,11,297,277,295,438,4,305,275,293,439,5,306,276,294,437,3,307,291,273,434,1,304,292,274,435,0,302,290,272,436,2,303,692,691,690,689,208,324,54,153,472,206,325,55,154,470,207,323,56,155,471,320,211,57,152,475,321,209,58,150,473,322,210,59,151,474,52,203,330,144,467,53,204,331,145,468,51,205,329,146,469,202,48,326,147,466,200,49,327,148,464,201,50,328,149,465,699,700,698,697,85,76,183,35,67,86,77,184,33,68,84,75,182,34,66,72,88,186,31,70,73,89,187,32,71,74,87,185,30,69,181,91,82,26,65,179,92,83,24,63,180,90,81,25,64,94,177,78,29,61,95,178,79,27,62,93,176,80,28,60,663,664,662,661,596,351,630,616,604,597,352,628,617,605,595,350,629,618,606,354,592,633,619,607,355,593,631,620,608,353,594,632,621,609,636,602,349,622,610,634,603,347,623,611,635,601,348,624,612,598,639,345,625,613,599,637,346,626,614,600,638,344,627,615,682,683,684,681,654,219,655,652,653,658,220,659,656,657,650,218,651,648,649,222,482,489,163,156,223,640,642,641,643,221,646,647,645,644,490,481,217,484,157,491,479,215,485,158,492,480,216,483,159,477,493,213,487,160,478,494,214,488,161,476,495,212,486,162,695,696,693,694,193,318,456,447,39,191,319,457,448,40,192,317,455,446,41,314,189,452,450,38,315,190,453,451,36,316,188,454,449,37,462,199,309,445,45,463,197,310,443,46,461,198,308,444,47,195,458,312,441,44,196,459,313,442,42,194,460,311,440,43,667,668,665,666,142,361,129,117,98,143,359,130,118,96,141,360,131,119,97,357,138,128,116,101,358,139,126,114,99,356,140,127,115,100,120,133,367,108,104,121,134,365,109,102,122,132,366,110,103,136,123,363,111,107,137,124,364,112,105,135,125,362,113,106,675,676,673,674 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#d5c298f3996cbe1c131ede943bdfb3db88b47e8bf729cba865448336ce4ceccf, 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 20:47:22 · history