Equation 677 Database

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Magma 1a7046e0fa7a…

magma 1a7046e0fa7a
Size
705
Isomorphism class hash
1a7046e0fa7a72db50565b57f04385724637922bdb9344e0d4cda8bbdd92f581
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 21:15:33
Display reorder
660,43,326,350,347,323,44,321,324,348,345,325,322,42,349,346,39,329,319,353,343,40,327,320,351,344,41,328,318,352,342,49,332,314,356,338,50,330,312,354,336,48,331,313,355,337,335,45,317,359,341,333,46,315,357,339,334,47,316,358,340,685,686,688,687,464,86,103,88,143,462,141,84,104,89,85,142,463,102,87,467,82,146,99,91,465,83,144,100,92,466,81,145,101,90,459,77,138,109,94,460,75,139,110,95,461,76,140,108,93,80,458,137,105,97,78,456,135,106,98,79,457,136,107,96,701,702,704,703,582,287,304,289,269,583,267,285,305,290,286,268,584,303,288,585,283,265,300,292,586,284,266,301,293,587,282,264,302,291,580,278,275,310,295,581,276,273,311,296,579,277,274,309,294,281,576,271,306,298,279,577,272,307,299,280,578,270,308,297,670,669,672,671,473,117,14,123,155,471,153,118,12,124,119,154,472,13,125,469,120,158,17,126,470,121,156,15,127,468,122,157,16,128,479,115,150,20,129,477,116,151,18,130,478,114,152,19,131,111,475,149,23,132,112,476,147,21,133,113,474,148,22,134,680,677,679,678,483,182,199,183,161,484,159,180,200,184,181,160,485,198,185,482,178,164,195,186,480,179,162,196,187,481,177,163,197,188,489,173,167,205,189,490,171,165,206,190,491,172,166,204,191,176,488,170,201,192,174,486,168,202,193,175,487,169,203,194,689,690,691,692,247,530,513,551,527,248,525,528,514,549,529,526,246,515,550,243,533,523,512,547,244,531,524,510,548,245,532,522,511,546,253,536,518,504,542,254,534,516,505,540,252,535,517,506,541,539,249,521,507,545,537,250,519,508,543,538,251,520,509,544,697,698,700,699,591,615,647,629,603,592,604,616,645,627,617,605,593,646,628,590,614,602,643,625,588,612,600,644,626,589,613,601,642,624,597,621,609,638,635,598,622,610,636,633,599,623,611,637,634,620,596,608,641,631,618,594,606,639,632,619,595,607,640,630,661,662,664,663,58,395,360,398,377,59,375,393,361,396,394,376,57,362,397,61,391,373,363,401,62,392,374,364,399,60,390,372,365,400,56,386,383,366,404,54,384,381,367,402,55,385,382,368,403,389,52,379,369,407,387,53,380,370,405,388,51,378,371,406,682,681,684,683,35,567,259,555,561,37,562,568,260,556,569,563,34,258,557,31,570,564,255,554,24,571,565,256,552,32,572,566,257,553,26,655,654,653,652,27,659,658,657,656,25,650,649,648,651,573,29,36,261,560,574,30,38,262,558,575,28,33,263,559,693,694,696,695,497,221,1,240,213,495,214,219,0,241,220,215,496,2,242,493,224,216,3,239,494,222,217,4,237,492,223,218,5,238,503,227,211,6,231,501,225,212,7,232,502,226,210,8,233,230,499,207,9,234,228,500,208,10,235,229,498,209,11,236,666,665,668,667,67,420,447,435,414,68,415,421,448,436,422,416,66,449,437,63,423,417,446,434,64,424,418,444,432,65,425,419,445,433,73,426,412,453,441,74,427,413,454,442,72,428,411,455,443,429,69,408,452,440,430,70,409,450,438,431,71,410,451,439,674,673,676,675 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#e1d7ea9e4f81623cd84c542145d634570787dd3fe7cd09a50189ca2a47386599, 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 21:15:34 · history