Equation 677 Database

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Magma e5ab918576e4…

magma e5ab918576e4
Size
705
Isomorphism class hash
e5ab918576e4dec79f92291015c4a24a7a33078794e2f6b4578b4414b5a88ff4
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 15:04:46
Display reorder
660,325,180,614,319,165,326,181,612,320,166,324,182,613,318,167,328,179,617,322,168,329,177,615,323,169,327,178,616,321,170,331,171,620,317,163,332,172,618,315,164,330,173,619,316,162,174,334,623,313,159,175,335,621,314,160,176,333,622,312,161,687,688,686,685,414,429,102,222,207,415,430,103,223,208,416,431,104,224,209,417,428,101,221,210,418,426,99,219,211,419,427,100,220,212,412,420,108,228,213,413,421,109,229,214,411,422,110,230,215,423,408,107,227,216,424,409,105,225,217,425,410,106,226,218,703,704,701,702,291,310,147,607,32,292,311,148,608,30,293,309,149,606,31,290,306,150,610,28,288,307,151,611,29,289,308,152,609,27,297,301,153,605,38,298,302,154,603,36,299,300,155,604,37,304,296,156,601,34,305,294,157,602,35,303,295,158,600,33,671,672,670,669,470,442,240,467,454,468,443,241,465,455,469,441,242,466,453,473,438,239,463,450,471,439,237,464,451,472,440,238,462,452,476,433,231,458,445,474,434,232,456,446,475,432,233,457,444,436,479,234,461,448,437,477,235,459,449,435,478,236,460,447,679,680,678,677,509,519,7,497,485,507,520,8,495,483,508,521,6,496,484,505,518,10,493,481,506,516,11,494,482,504,517,9,492,480,515,525,13,503,491,513,526,14,501,489,514,527,12,502,490,524,511,16,499,487,522,512,17,500,488,523,510,15,498,486,692,691,690,689,111,584,126,270,255,112,582,127,271,256,113,583,128,272,257,114,587,125,269,258,115,585,123,267,259,116,586,124,268,260,117,579,132,276,261,118,580,133,277,262,119,581,134,278,263,578,120,131,275,264,576,121,129,273,265,577,122,130,274,266,699,700,698,697,62,65,88,42,77,60,63,89,43,75,61,64,87,44,76,58,68,91,41,80,59,66,92,39,78,57,67,90,40,79,53,71,94,48,83,51,69,95,49,81,52,70,93,50,82,74,56,97,47,86,72,54,98,45,84,73,55,96,46,85,663,664,662,661,638,346,187,631,358,636,347,188,632,359,637,345,186,630,357,641,342,183,634,354,639,343,184,635,355,640,344,185,633,356,644,337,193,629,349,642,338,194,627,350,643,336,192,628,348,340,647,189,625,352,341,645,190,626,353,339,646,191,624,351,682,683,684,681,142,146,595,281,24,143,144,596,279,25,141,145,594,280,26,658,656,598,659,657,648,649,599,650,651,654,652,597,655,653,140,20,593,284,4,138,18,591,282,5,139,19,592,283,3,23,136,589,287,1,21,137,590,285,0,22,135,588,286,2,695,696,693,694,557,569,253,545,533,555,567,254,543,531,556,568,252,544,532,553,565,249,541,529,554,566,250,542,530,552,564,251,540,528,563,575,244,551,539,561,573,245,549,537,562,574,243,550,538,571,559,247,547,535,572,560,248,548,536,570,558,246,546,534,667,668,665,666,363,382,196,407,394,364,383,197,405,395,365,381,195,406,393,362,378,199,403,390,360,379,200,404,391,361,380,198,402,392,369,373,202,398,385,370,374,203,396,386,371,372,201,397,384,376,368,205,401,388,377,366,206,399,389,375,367,204,400,387,675,676,673,674 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#02a5eb7a1dc0484d80c271e9dde4b7cc0db9de7edd8cff390e9bbef93843b6b3, 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 15:04:50 · history