Equation 677 Database

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Magma 9e25855a176c…

magma 9e25855a176c
Size
705
Isomorphism class hash
9e25855a176c80a4be795ade517f7906d90462092a74907e4866c55e14dd09f7
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 19:18:38
Display reorder
660,306,330,316,292,341,293,307,331,317,339,332,291,308,315,340,295,305,329,319,344,296,303,327,320,342,294,304,328,318,343,312,336,322,298,347,313,337,323,299,345,314,338,321,297,346,311,335,325,301,350,309,333,326,302,348,310,334,324,300,349,685,686,688,687,210,278,263,457,281,458,211,276,261,279,277,456,212,262,280,453,209,274,266,284,454,207,275,264,282,455,208,273,265,283,216,269,258,448,287,217,267,259,449,285,218,268,260,447,286,215,272,257,451,290,213,270,255,452,288,214,271,256,450,289,701,702,704,703,603,587,612,27,588,28,604,585,613,589,586,29,605,614,590,26,602,583,615,591,24,600,584,616,592,25,601,582,617,593,609,578,618,18,594,610,576,619,19,595,611,577,620,20,596,608,581,621,21,597,606,579,622,22,598,607,580,623,23,599,670,669,672,671,89,465,91,219,481,220,87,466,92,482,467,221,88,90,480,222,85,468,94,477,223,86,469,95,478,224,84,470,93,479,80,463,97,225,472,78,464,98,226,473,79,462,96,227,471,83,459,100,228,475,81,460,101,229,476,82,461,99,230,474,680,677,679,678,489,232,505,109,248,110,490,233,506,246,231,108,491,504,247,112,492,235,501,244,113,493,236,502,245,111,494,234,503,243,487,238,496,107,254,488,239,497,105,252,486,237,495,106,253,483,241,499,103,250,484,242,500,104,251,485,240,498,102,249,689,690,691,692,534,558,544,170,520,168,535,559,545,521,560,169,536,543,519,173,533,557,547,523,171,531,555,548,524,172,532,556,546,522,540,564,550,165,526,541,565,551,166,527,542,566,549,167,525,539,563,553,164,529,537,561,554,162,530,538,562,552,163,528,697,698,700,699,630,57,647,41,44,39,631,58,645,42,59,40,632,646,43,37,633,56,643,47,38,634,54,644,45,36,635,55,642,46,628,63,638,32,50,629,64,636,30,48,627,65,637,31,49,624,62,641,35,53,625,60,639,33,51,626,61,640,34,52,661,662,664,663,363,389,378,11,354,9,364,387,379,355,388,10,365,380,356,7,366,392,377,353,8,367,390,375,351,6,368,391,376,352,369,395,384,17,360,370,393,385,15,361,371,394,386,16,362,372,398,383,13,359,373,396,381,14,357,374,397,382,12,358,682,681,684,683,178,189,1,66,570,67,179,190,0,571,191,68,177,2,572,69,174,188,3,573,70,175,186,4,574,71,176,187,5,575,652,654,653,72,655,656,658,657,73,659,648,650,649,74,651,180,194,184,75,569,181,192,185,76,567,182,193,183,77,568,693,694,696,695,138,122,153,516,137,517,139,120,154,135,121,518,140,155,136,515,141,125,152,133,513,142,123,150,134,514,143,124,151,132,144,117,159,507,128,145,118,160,508,126,146,119,161,509,127,147,116,158,510,131,148,114,156,511,129,149,115,157,512,130,666,665,668,667,420,438,424,195,406,196,421,439,425,407,440,197,422,423,405,198,419,437,427,409,199,417,435,428,410,200,418,436,426,408,411,444,430,201,404,412,445,431,202,402,413,446,429,203,403,414,443,433,204,400,415,441,434,205,401,416,442,432,206,399,674,673,676,675 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#9c565a9fd79b154e390f38dd387d90fedf9817e0675733b83815c4693870456f, 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 19:18:39 · history