Equation 677 Database

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Magma fa9abef110ec…

magma fa9abef110ec
Size
705
Isomorphism class hash
fa9abef110ec41de9a6d60c67b08af7b668eba508cc9603a2e33a28f685568f1
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 16:37:32
Display reorder
660,40,365,366,586,350,367,363,41,587,348,39,364,585,349,368,361,36,369,582,353,362,37,370,583,351,360,38,371,584,352,372,31,577,356,345,373,32,578,354,346,374,30,576,355,347,34,375,580,359,344,35,376,581,357,342,33,377,579,358,343,687,688,686,685,422,438,142,252,437,143,439,420,253,435,421,440,254,436,141,441,425,138,255,433,442,423,139,256,434,443,424,140,257,432,133,417,258,444,428,134,418,259,445,426,132,419,260,446,427,416,136,261,447,431,414,137,262,448,429,415,135,263,449,430,703,704,701,702,557,95,546,330,568,547,93,555,331,569,556,94,332,567,548,91,553,549,333,564,92,554,550,334,565,90,552,551,335,566,544,563,336,86,574,545,561,337,84,575,543,562,338,85,573,559,540,339,89,570,560,541,340,87,571,558,542,341,88,572,671,672,670,669,462,277,457,161,271,458,278,463,159,272,464,276,160,270,456,280,465,460,157,274,281,466,461,158,275,279,467,459,156,273,455,468,167,283,269,453,469,165,284,267,454,470,166,282,268,471,451,163,286,265,472,452,164,287,266,473,450,162,285,264,679,680,678,677,195,179,181,481,294,182,177,196,482,295,197,178,480,296,180,175,194,184,484,297,176,192,185,485,298,174,193,183,483,299,187,201,479,170,292,188,202,477,168,293,186,203,478,169,291,200,190,475,173,288,198,191,476,171,289,199,189,474,172,290,692,691,690,689,224,102,77,525,318,75,103,222,526,319,223,104,527,320,76,105,227,73,524,321,106,225,74,522,322,107,226,72,523,323,83,219,531,100,316,81,220,532,101,317,82,221,533,99,315,218,79,530,96,312,216,80,528,97,313,217,78,529,98,314,699,700,698,697,48,12,2,27,62,1,13,49,28,66,50,14,29,70,0,11,51,5,26,67,9,52,3,24,71,10,53,4,25,63,8,46,18,64,59,6,47,19,68,55,7,45,20,61,57,42,65,21,17,54,43,69,22,15,56,44,60,23,16,58,663,664,662,661,593,623,626,380,603,624,621,591,378,604,592,622,379,605,625,619,589,629,383,602,620,590,627,381,600,618,588,628,382,601,632,599,386,614,609,630,597,384,612,610,631,598,385,613,611,595,635,389,617,608,596,633,387,615,606,594,634,388,616,607,682,683,684,681,650,649,651,236,648,655,653,654,234,652,658,656,235,657,659,646,645,647,239,644,636,637,638,237,639,642,640,643,238,641,537,110,231,329,115,538,108,232,327,116,539,109,233,328,114,113,536,230,325,118,111,534,228,326,119,112,535,229,324,117,695,696,693,694,209,499,515,302,493,513,500,207,300,494,208,498,301,492,514,502,205,511,305,496,503,206,512,303,497,501,204,510,304,495,521,215,308,505,491,519,213,306,506,489,520,214,307,504,490,211,517,311,508,487,212,518,309,509,488,210,516,310,507,486,667,668,665,666,147,398,413,128,248,411,396,148,126,246,149,397,127,247,412,401,146,409,131,251,399,144,410,129,249,400,145,408,130,250,404,153,123,393,243,402,154,124,394,244,403,155,125,395,245,152,407,122,392,242,150,405,120,390,240,151,406,121,391,241,675,676,673,674 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#37e131d0061e11ac6a08c1b5043c4a4bd1e23715ce44e1796d2c3958c15ae4cf, 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 16:37:33 · history