Equation 677 Database

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Magma 06725a11460c…

magma 06725a11460c
Size
705
Isomorphism class hash
06725a11460c54d9e439c92fce57ff46acdae264f54860398c142025d9820d6a
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 19:54:58
Display reorder
660,99,81,223,232,102,100,82,224,233,103,101,83,222,231,104,80,98,226,228,105,78,96,227,229,106,79,97,225,230,107,90,87,221,238,108,91,88,219,239,109,92,89,220,237,110,86,93,217,234,111,84,94,218,235,112,85,95,216,236,113,685,686,688,687,57,333,337,307,315,58,334,338,308,316,59,335,336,306,317,332,56,340,310,314,330,54,341,311,312,331,55,339,309,313,63,324,343,305,321,64,325,344,303,322,65,326,342,304,323,327,62,346,301,320,328,60,347,302,318,329,61,345,300,319,701,702,704,703,214,563,575,585,551,215,561,573,586,549,213,562,574,587,550,559,210,571,584,547,560,211,572,582,548,558,212,570,583,546,205,554,566,576,542,206,552,564,577,540,204,553,565,578,541,557,208,569,579,545,555,209,567,580,543,556,207,568,581,544,670,669,672,671,4,359,371,383,393,5,357,369,381,394,3,358,370,382,395,355,1,367,379,392,356,0,368,380,390,354,2,366,378,391,10,350,362,374,384,11,348,360,372,385,9,349,361,373,386,353,6,365,377,387,351,7,363,375,388,352,8,364,376,389,680,677,679,678,168,407,419,431,441,169,405,417,429,442,170,406,418,430,443,403,167,415,427,440,404,165,416,428,438,402,166,414,426,439,159,398,410,422,432,160,396,408,420,433,161,397,409,421,434,401,162,413,425,435,399,163,411,423,436,400,164,412,424,437,689,690,691,692,186,141,499,507,527,187,142,500,508,525,188,143,498,509,526,140,185,502,506,523,138,183,503,504,524,139,184,501,505,522,192,147,497,513,518,193,148,495,514,516,194,149,496,515,517,146,191,493,512,521,144,189,494,510,519,145,190,492,511,520,697,698,700,699,598,635,647,602,623,599,633,645,600,621,597,634,646,601,622,631,594,643,605,619,632,595,644,603,620,630,596,642,604,618,589,626,638,608,614,590,624,636,606,612,588,625,637,607,613,629,592,641,611,617,627,593,639,609,615,628,591,640,610,616,661,662,664,663,125,273,278,247,255,123,274,276,248,256,124,275,277,246,257,272,121,281,250,254,270,122,279,251,252,271,120,280,249,253,116,264,284,245,261,114,265,282,243,262,115,266,283,244,263,267,119,287,241,260,268,117,285,242,258,269,118,286,240,259,682,681,684,683,528,200,28,40,154,529,198,29,41,155,530,199,27,39,153,203,531,24,36,157,201,532,25,37,158,202,533,26,38,156,534,655,652,653,654,535,659,656,657,658,536,650,648,649,651,197,537,30,34,152,195,538,31,35,150,196,539,32,33,151,693,694,696,695,182,468,484,447,466,180,469,485,448,467,181,470,483,449,465,471,178,480,446,462,472,179,481,444,463,473,177,482,445,464,173,474,490,453,457,171,475,491,454,458,172,476,489,455,456,477,176,486,452,460,478,174,487,450,461,479,175,488,451,459,666,665,668,667,51,294,73,132,17,52,295,74,133,15,53,296,72,134,16,297,50,76,135,13,298,48,77,136,14,299,49,75,137,12,42,292,71,130,23,43,293,69,131,21,44,291,70,129,22,288,45,67,126,19,289,46,68,127,20,290,47,66,128,18,674,673,676,675 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#b3dac6ff36f26cacc8049b7c1e09fd794a0277a3d237510b4c6377f158398334, 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 19:54:59 · history