Equation 677 Database

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Magma d219463ad892…

magma d219463ad892
Size
705
Isomorphism class hash
d219463ad8923638c3ed5be2ec06b22cd10425134108ad895ec06e5f671df4a7
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 21:09:48
Display reorder
660,333,3,117,126,340,331,0,115,124,341,332,2,116,125,342,336,6,122,339,120,334,118,4,123,337,5,119,335,121,338,9,112,132,328,346,7,113,130,329,347,8,114,131,330,348,12,111,128,327,345,109,10,129,325,343,326,110,11,127,344,685,686,688,687,389,196,418,375,398,390,197,419,373,399,388,198,420,374,397,385,195,378,401,417,386,415,193,376,402,194,416,387,377,400,202,409,381,395,404,203,410,379,396,405,204,411,380,394,403,201,412,384,391,407,413,199,382,392,408,393,414,200,383,406,701,702,704,703,315,608,289,312,288,313,609,290,310,286,314,610,291,311,287,318,611,308,284,292,316,293,612,309,285,613,294,317,307,283,614,295,303,321,279,615,296,301,319,277,616,297,302,320,278,617,298,306,324,282,299,618,304,322,280,323,300,619,305,281,670,669,672,671,428,207,450,40,435,429,205,448,41,433,427,206,449,42,434,431,210,39,438,446,432,447,208,37,436,209,445,430,38,437,213,456,46,426,441,211,454,47,424,439,212,455,48,425,440,216,452,45,422,444,453,214,43,423,442,421,451,215,44,443,680,677,679,678,485,228,462,474,493,486,226,460,472,494,484,227,461,473,495,481,224,470,496,458,482,459,225,471,497,223,457,483,469,498,219,468,480,491,499,217,466,478,492,500,218,467,479,490,501,222,464,476,487,502,465,220,477,488,503,489,463,221,475,504,689,690,691,692,530,253,555,528,552,531,254,553,526,550,529,255,554,527,551,533,256,524,548,558,534,556,257,525,549,258,557,532,523,547,259,561,519,536,543,260,559,517,537,541,261,560,518,535,542,262,564,522,539,546,562,263,520,540,544,538,563,264,521,545,697,698,700,699,627,20,655,25,632,628,21,653,26,633,626,19,654,27,634,630,23,28,635,651,631,652,24,29,636,22,650,629,30,637,18,646,31,625,638,16,644,32,623,639,17,645,33,624,640,14,649,34,621,641,647,15,35,622,642,620,648,13,36,643,661,662,664,663,145,355,171,144,168,146,356,169,142,166,147,357,170,143,167,148,358,140,164,174,149,172,359,141,165,360,173,150,139,163,353,177,135,151,159,354,175,133,152,157,352,176,134,153,158,349,180,138,154,162,178,350,136,155,160,156,179,351,137,161,682,681,684,683,585,270,607,568,587,583,268,605,569,588,584,269,606,570,589,581,266,567,590,603,582,604,267,565,591,265,602,580,566,592,276,598,574,576,593,274,597,575,1,586,275,658,656,657,659,272,601,573,579,594,599,273,571,577,595,578,600,271,572,596,693,694,696,695,66,505,241,54,236,64,506,242,52,237,65,507,243,53,235,62,508,50,239,244,63,245,509,51,240,510,246,61,49,238,511,247,60,72,234,512,248,58,70,232,513,249,59,71,233,514,250,56,68,230,251,515,57,69,231,67,252,516,55,229,666,665,668,667,75,365,89,98,189,73,366,90,99,187,74,364,88,97,188,78,361,101,192,85,76,86,362,102,190,363,87,77,100,191,371,95,104,81,184,372,96,105,79,185,370,94,103,80,186,367,91,107,84,183,92,368,108,82,181,83,93,369,106,182,674,673,676,675 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#dc2fe3473be348561d898626a2f45bbebd7964bafd5487f2fff34f8adc67b3cf, 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 21:09:49 · history