Equation 677 Database

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Magma 7ec8e6bfd91b…

magma 7ec8e6bfd91b
Size
705
Isomorphism class hash
7ec8e6bfd91b68caedb523138fcb6314a523b943e0ffe1d171218331c4d47d64
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 15:29:12
Display reorder
660,156,368,177,171,186,157,369,178,172,187,367,179,173,158,188,364,159,176,170,189,365,160,174,168,190,366,161,175,169,191,154,183,162,374,192,155,184,163,375,193,153,185,164,373,194,150,182,165,370,195,151,180,166,371,196,152,181,167,372,197,685,686,688,687,310,31,408,329,301,311,32,406,327,302,33,407,328,309,300,34,306,411,325,304,35,307,409,326,305,36,308,410,324,303,316,403,320,29,299,317,404,318,30,297,315,405,319,28,298,312,402,323,25,295,313,400,321,26,296,314,401,322,27,294,701,702,704,703,595,352,572,604,591,596,353,573,605,589,354,571,606,597,590,355,594,568,607,587,356,592,569,608,588,357,593,570,609,586,601,578,610,358,582,602,579,611,359,580,603,577,612,360,581,600,574,613,361,585,598,575,614,362,583,599,576,615,363,584,670,669,672,671,43,330,95,420,0,44,331,93,418,2,332,94,419,45,3,333,46,91,423,4,334,47,92,421,5,335,48,90,422,6,41,101,415,336,7,42,99,416,337,8,40,100,417,338,9,37,97,414,339,10,38,98,412,340,11,39,96,413,341,12,680,677,679,678,105,16,445,430,452,106,17,446,431,453,18,447,432,107,451,15,104,444,433,448,13,102,442,434,449,14,103,443,435,450,111,436,428,22,458,112,437,429,23,459,113,438,427,24,457,110,439,424,21,454,108,440,425,19,455,109,441,426,20,456,689,690,691,692,545,52,529,514,535,546,53,530,515,536,54,531,516,544,537,51,548,528,517,534,49,549,526,518,532,50,547,527,519,533,551,520,512,58,541,552,521,513,59,542,550,522,511,60,543,554,523,508,57,540,555,524,509,55,538,553,525,510,56,539,697,698,700,699,623,128,651,632,138,624,126,649,633,139,127,650,631,622,140,131,626,647,628,141,129,627,648,629,142,130,625,646,630,143,621,642,638,134,144,619,640,639,132,145,620,641,637,133,146,617,645,634,137,147,618,643,635,135,148,616,644,636,136,149,661,662,664,663,209,383,223,213,236,207,384,224,214,234,382,222,215,208,235,386,205,226,212,239,387,206,227,210,237,385,204,225,211,238,200,229,219,381,242,198,230,220,379,240,199,228,221,380,241,203,232,218,377,245,201,233,216,378,243,202,231,217,376,244,682,681,684,683,77,556,351,86,71,78,557,349,84,72,558,350,85,79,73,559,76,347,89,70,560,74,348,87,68,561,75,346,88,69,658,659,656,562,657,83,342,61,563,1,652,654,653,564,655,82,345,63,565,65,80,343,64,566,66,81,344,62,567,67,693,694,696,695,495,117,471,500,476,493,118,469,501,477,119,470,499,494,475,116,491,467,496,472,114,492,468,497,473,115,490,466,498,474,486,462,506,123,482,484,460,507,124,483,485,461,505,125,481,489,465,502,122,478,487,463,503,120,479,488,464,504,121,480,666,665,668,667,293,391,262,253,280,291,392,263,254,281,393,261,252,292,279,390,289,258,256,276,388,290,259,257,277,389,288,260,255,278,284,268,251,397,271,282,269,249,398,272,283,267,250,399,270,287,264,247,396,274,285,265,248,394,275,286,266,246,395,273,674,673,676,675 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#1c6b3e96bd585e9e8fd52e93592fcd11cb6c83a04227bfcba3bf653b0809cf1c, 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 15:29:13 · history