Equation 677 Database

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Magma ab6db65751f3…

magma ab6db65751f3
Size
705
Isomorphism class hash
ab6db65751f39ce08aeb3d211e225990db960dafcb7fd18beaf2b8d6b4cbdbd5
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 16:28:18
Display reorder
660,376,62,365,378,353,377,60,379,363,351,375,61,380,364,352,65,372,381,361,349,63,373,382,362,350,64,374,383,360,348,367,356,68,384,344,368,354,66,385,342,366,355,67,386,343,359,370,71,387,347,357,371,69,388,345,358,369,70,389,346,685,686,688,687,450,14,488,466,484,451,12,467,486,485,452,13,465,487,483,17,453,462,491,480,15,454,463,489,481,16,455,464,490,482,456,494,20,472,475,457,492,18,473,476,458,493,19,471,474,497,459,23,468,478,495,460,21,469,479,496,461,22,470,477,701,702,704,703,333,158,611,130,594,334,156,131,609,595,335,157,129,610,596,161,332,126,607,597,159,330,127,608,598,160,331,128,606,599,339,602,164,121,592,340,600,162,122,593,341,601,163,120,591,605,338,167,124,588,603,336,165,125,589,604,337,166,123,590,670,669,672,671,30,136,262,505,512,31,137,506,263,510,32,135,504,261,511,132,33,508,258,515,133,34,509,259,513,134,35,507,260,514,28,268,142,503,518,29,269,143,501,516,27,267,141,502,517,264,24,138,499,521,265,25,139,500,519,266,26,140,498,520,680,677,679,678,530,281,215,537,546,528,279,538,213,547,529,280,539,214,548,277,533,536,211,549,278,531,534,212,550,276,532,535,210,551,525,206,272,543,552,526,204,270,544,553,527,205,271,545,554,209,524,275,542,555,207,522,273,540,556,208,523,274,541,557,689,690,691,692,237,49,307,7,576,238,50,8,308,577,239,48,6,306,578,52,236,10,310,579,53,234,11,311,580,51,235,9,309,581,228,313,55,5,574,229,314,56,3,575,230,312,54,4,573,316,231,58,0,570,317,232,59,2,571,315,233,57,1,572,697,698,700,699,194,168,635,183,618,192,169,184,633,619,193,170,185,634,620,171,197,182,631,621,172,195,180,632,622,173,196,181,630,623,200,626,174,189,616,198,624,175,190,617,199,625,176,191,615,629,203,177,188,612,627,201,178,186,613,628,202,179,187,614,661,662,664,663,41,390,105,78,95,39,391,79,106,93,40,392,80,107,94,393,37,81,104,91,394,38,82,102,92,395,36,83,103,90,47,96,396,76,86,45,97,397,77,84,46,98,398,75,85,99,43,399,72,89,100,44,400,73,87,101,42,401,74,88,682,681,684,683,241,319,584,248,255,242,320,246,582,256,240,318,247,583,257,322,244,251,587,254,323,245,249,585,252,321,243,250,586,253,642,643,325,641,640,646,647,326,645,644,637,638,324,636,639,655,654,328,652,653,659,658,329,657,656,651,650,327,648,649,693,694,696,695,224,560,294,151,289,222,558,152,295,290,223,559,150,296,288,563,227,154,297,292,561,225,155,298,293,562,226,153,299,291,219,300,566,149,287,220,301,564,147,285,221,302,565,148,286,303,218,569,145,283,304,216,567,146,284,305,217,568,144,282,666,665,668,667,405,117,448,414,430,406,118,415,449,431,407,119,416,447,429,116,404,417,444,426,114,402,418,445,427,115,403,419,446,428,411,439,108,420,436,412,440,109,421,437,413,438,110,422,435,442,410,111,423,432,443,408,112,424,433,441,409,113,425,434,674,673,676,675 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#33430dadf8546adceaddacfc75eeb6c00258f5413ce1926e16e948db7c79b4f3, 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 16:28:19 · history