Equation 677 Database

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Magma 553250fdde1b…

magma 553250fdde1b
Size
705
Isomorphism class hash
553250fdde1b50ac8f2e626e920b5eac1d9a00d69690037dabf8d7cb06b6a927
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 21:19:40
Display reorder
704,76,44,53,66,77,42,67,51,75,43,68,52,72,47,49,69,73,45,50,70,74,46,71,48,82,39,59,64,40,83,65,57,41,81,63,58,38,78,55,60,36,79,61,56,80,37,62,54,95,93,94,91,92,90,86,84,88,89,87,85,683,680,682,681,2,158,529,551,1,156,549,530,0,157,550,528,5,161,532,547,3,159,533,548,4,160,546,531,8,164,535,542,162,6,540,536,163,7,541,534,167,11,538,545,165,9,543,539,10,166,544,537,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,453,26,430,435,454,24,436,431,455,25,437,429,452,29,426,434,450,27,427,432,451,28,433,428,444,32,421,441,30,445,442,422,31,446,443,420,35,447,424,440,33,448,438,425,449,34,439,423,456,457,458,459,460,461,462,463,467,465,466,464,669,671,668,670,361,239,337,359,362,237,357,338,360,238,358,336,364,235,340,355,365,236,341,356,363,234,354,339,367,230,343,350,228,368,348,344,229,366,349,342,233,370,346,353,231,371,351,347,369,232,352,345,334,335,333,330,331,332,325,326,327,328,329,324,679,676,678,677,126,527,154,109,127,525,110,155,128,526,108,153,129,523,150,112,130,524,151,113,131,522,111,152,124,518,145,115,516,125,116,146,517,123,114,144,521,120,148,118,519,121,119,149,122,520,117,147,137,135,136,133,134,132,143,141,138,139,140,142,689,690,688,691,615,18,638,607,616,19,608,636,617,20,606,637,614,21,641,610,612,22,639,611,613,23,609,640,621,16,644,605,17,622,603,642,15,623,604,643,12,620,647,601,13,618,602,645,619,14,600,646,633,634,635,632,630,631,624,625,629,627,628,626,692,694,693,695,512,100,486,494,510,101,492,487,511,99,493,488,515,96,489,497,513,97,490,495,514,98,496,491,507,106,484,500,107,508,498,485,105,509,499,483,102,506,480,503,103,504,501,481,505,104,502,482,469,470,468,472,473,471,475,476,477,478,479,474,661,662,660,663,288,263,265,286,289,261,287,266,290,262,285,264,291,259,268,282,292,260,269,283,293,258,284,267,294,254,271,277,252,295,278,272,253,296,276,270,257,297,274,280,255,298,281,275,299,256,279,273,306,307,308,309,310,311,304,305,302,300,301,303,685,686,684,687,215,318,189,197,213,319,195,190,214,320,196,191,211,321,188,193,212,322,186,194,210,323,192,187,206,316,180,203,317,204,201,181,315,205,202,182,312,209,183,199,313,207,200,184,208,314,198,185,216,217,218,219,220,221,222,223,227,225,226,224,698,697,699,696,376,241,396,418,377,242,419,397,375,240,417,398,372,244,399,414,373,245,400,415,374,243,416,401,382,247,402,409,248,383,410,403,246,381,408,404,250,378,405,412,251,379,413,406,380,249,411,407,395,393,394,391,392,390,386,384,388,389,387,385,666,665,667,664,595,169,570,577,596,170,578,571,594,168,576,572,598,172,573,580,599,173,574,581,597,171,579,575,593,175,568,583,176,591,584,569,174,592,582,567,178,589,564,586,179,590,587,565,588,177,585,566,552,553,554,555,556,557,558,559,563,561,562,560,674,673,675,672 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#e9460cea3e471d03fe1a4dfa5e68e64aa509c8601c2a885c863435b22f6faffe, 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 21:19:41 · history