Equation 677 Database

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Magma c1b8dc3495fd…

magma c1b8dc3495fd
Size
705
Isomorphism class hash
c1b8dc3495fd12b321685c77889ed22dcdaf27257ece8162c4656b6949dafad4
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 18:13:44
Display reorder
660,321,309,367,333,346,322,310,334,368,347,323,311,366,335,345,312,324,363,336,349,313,325,364,337,350,314,326,365,338,348,327,315,358,339,352,328,316,359,340,353,329,317,357,341,351,318,330,361,342,355,319,331,362,343,356,320,332,360,344,354,685,686,688,687,452,479,109,457,465,450,477,458,110,466,451,478,111,456,467,482,448,112,453,468,480,449,113,454,469,481,447,114,455,470,443,485,115,463,471,441,483,116,464,472,442,484,117,462,473,488,446,118,459,474,486,444,119,460,475,487,445,120,461,476,701,702,704,703,583,577,300,603,562,584,578,601,301,563,585,579,302,602,564,576,582,299,599,565,574,580,297,600,566,575,581,298,598,567,589,568,306,594,560,590,569,307,592,561,591,570,308,593,559,571,588,305,597,556,572,586,303,595,557,573,587,304,596,558,670,669,672,671,100,137,226,496,129,101,138,497,227,127,102,136,225,495,128,133,99,229,499,132,134,97,230,500,130,135,98,228,498,131,106,143,232,494,124,107,144,233,492,125,108,142,231,493,126,139,105,235,490,123,140,103,236,491,121,141,104,234,489,122,680,677,679,678,94,522,156,244,507,95,523,245,154,508,96,524,155,243,509,521,93,152,247,510,519,91,153,248,511,520,92,151,246,512,85,513,147,242,505,86,514,145,240,506,87,515,146,241,504,516,88,150,238,501,517,89,148,239,502,518,90,149,237,503,689,690,691,692,278,269,204,53,545,276,267,54,202,543,277,268,203,52,544,272,274,200,49,548,270,275,201,50,546,271,273,199,51,547,284,264,195,59,540,282,265,193,60,541,283,266,194,58,542,263,280,198,55,539,261,281,196,56,537,262,279,197,57,538,697,698,700,699,4,81,639,612,619,5,79,610,637,620,6,80,638,611,621,84,3,635,615,618,82,0,636,613,616,83,2,634,614,617,10,76,630,607,625,11,77,628,608,626,12,78,629,609,627,75,9,633,606,624,73,7,631,604,622,74,8,632,605,623,661,662,664,663,392,375,29,65,22,390,376,66,30,23,391,377,28,64,24,378,388,25,61,21,379,389,26,62,19,380,387,27,63,20,383,373,35,71,13,381,374,36,72,14,382,372,34,70,15,369,386,31,67,16,370,384,32,68,17,371,385,33,69,18,682,681,684,683,206,221,293,552,217,207,222,550,291,215,208,223,292,551,216,220,209,296,555,213,218,210,294,553,214,219,211,295,554,212,644,646,288,647,645,205,224,289,549,1,641,640,290,642,643,658,656,287,659,657,650,648,285,651,649,654,652,286,655,653,693,694,696,695,173,166,527,182,257,174,167,183,525,255,172,168,526,181,256,165,169,530,185,260,163,170,528,186,258,164,171,529,184,259,179,157,533,188,252,180,158,531,189,253,178,159,532,187,254,160,175,536,191,251,161,176,534,192,249,162,177,535,190,250,666,665,668,667,438,418,37,401,410,439,419,399,38,408,440,417,39,400,409,421,437,40,404,406,422,435,41,402,407,420,436,42,403,405,429,424,43,396,416,430,425,44,397,414,431,423,45,398,415,427,432,46,395,412,428,433,47,393,413,426,434,48,394,411,674,673,676,675 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#6da5e6765bc0adc27e9eb05052cc3d9b74fd6a5fdc541eafc0e7aaffee5eac36, 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 18:13:45 · history