Equation 677 Database

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Magma 12751dbe80b7…

magma 12751dbe80b7
Size
705
Isomorphism class hash
12751dbe80b71313e46779ef78dfbf8e14526814084841853362d71b5bf4885b
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 19:42:49
Display reorder
660,280,369,292,303,356,370,281,293,304,354,279,371,291,305,355,276,368,288,302,359,277,366,289,300,357,278,367,290,301,358,286,360,309,298,351,287,361,310,299,352,285,362,311,297,353,363,282,308,294,350,364,283,306,295,348,365,284,307,296,349,685,686,688,687,134,11,440,216,167,9,132,438,217,165,133,10,439,218,166,137,7,443,219,163,135,8,441,220,164,136,6,442,221,162,140,2,222,435,158,138,1,223,436,156,139,0,224,437,157,5,143,225,434,161,3,141,226,432,159,4,142,227,433,160,701,702,704,703,336,579,599,562,566,580,337,597,563,564,338,581,598,561,565,339,578,595,558,569,340,576,596,559,567,341,577,594,560,568,342,585,553,590,572,343,586,554,588,570,344,587,552,589,571,584,345,556,593,575,582,346,557,591,573,583,347,555,592,574,670,669,672,671,148,243,263,451,235,244,149,261,452,236,147,245,262,450,234,144,242,259,454,238,145,240,260,455,239,146,241,258,453,237,154,249,449,254,233,155,250,447,252,231,153,251,448,253,232,248,150,445,257,229,246,151,446,255,230,247,152,444,256,228,680,677,679,678,75,479,274,131,464,477,76,275,129,462,77,478,273,130,463,74,475,270,127,467,72,476,271,128,465,73,474,272,126,466,81,470,122,265,459,82,468,120,266,460,83,469,121,264,461,473,80,125,268,458,471,78,123,269,456,472,79,124,267,457,689,690,691,692,22,498,504,527,68,499,23,505,525,66,21,500,506,526,67,18,501,507,523,71,19,502,508,524,69,20,503,509,522,70,13,496,518,510,63,14,497,516,511,64,12,495,517,512,65,492,16,521,513,62,493,17,519,514,60,494,15,520,515,61,697,698,700,699,111,615,635,98,607,616,112,633,96,608,113,617,634,97,606,110,614,631,101,610,108,612,632,99,611,109,613,630,100,609,117,621,104,626,605,118,622,102,624,603,119,623,103,625,604,620,116,107,629,601,618,114,105,627,602,619,115,106,628,600,661,662,664,663,319,413,375,395,398,411,320,376,393,396,318,412,377,394,397,322,409,374,391,401,323,410,372,392,399,321,408,373,390,400,317,419,386,381,404,315,417,384,382,402,316,418,385,383,403,415,313,389,380,407,416,314,387,378,405,414,312,388,379,406,682,681,684,683,334,537,542,550,533,538,335,540,551,531,333,539,541,549,532,330,536,545,546,529,331,534,543,547,530,332,535,544,548,528,325,642,643,640,641,326,646,647,644,645,324,636,638,637,639,654,328,655,653,652,658,329,659,656,657,650,327,651,649,648,693,694,696,695,88,32,46,50,488,30,89,47,48,486,87,31,45,49,487,84,35,42,53,491,85,33,43,51,489,86,34,44,52,490,94,27,56,37,483,95,28,54,38,484,93,29,55,36,485,26,90,59,40,482,24,91,57,41,480,25,92,58,39,481,666,665,668,667,426,172,183,203,204,173,427,184,201,205,428,171,185,202,206,429,168,182,199,207,430,169,180,200,208,431,170,181,198,209,424,178,194,189,210,425,179,192,190,211,423,177,193,191,212,174,420,197,188,213,175,421,195,186,214,176,422,196,187,215,674,673,676,675 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#a559a3aef5c48d7617a1f37068ce834508ecbb6c78b3262065881b6dd2cda018, 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 19:42:50 · history