Equation 677 Database

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Magma c84126bd2de0…

magma c84126bd2de0
Size
705
Isomorphism class hash
c84126bd2de0afda7b1aeec50e37d1ba5be73ea19cf82146fc283468414319bf
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 20:43:18
Display reorder
660,67,349,131,76,340,68,132,77,341,350,66,348,130,75,339,134,70,345,72,343,71,135,346,73,344,69,133,347,74,342,65,137,355,82,338,83,63,138,356,336,64,136,354,81,337,140,61,351,78,334,141,62,352,79,335,139,60,353,80,333,685,686,688,687,264,461,208,217,243,265,209,218,244,459,266,460,207,216,245,211,263,464,213,246,261,212,462,214,247,262,210,463,215,248,270,206,456,223,241,224,271,204,457,242,272,205,458,222,240,202,269,455,219,237,203,267,453,220,238,201,268,454,221,239,701,702,704,703,321,616,631,125,59,322,629,126,57,614,323,615,630,124,58,627,324,619,128,55,325,628,617,129,56,326,626,618,127,54,327,622,611,123,50,121,328,620,612,48,329,621,613,122,49,625,330,610,119,53,623,331,608,120,51,624,332,609,118,52,670,669,672,671,278,472,482,235,198,276,480,236,199,473,277,471,481,234,200,478,274,475,231,197,275,479,476,232,195,273,477,474,233,196,284,488,470,226,189,227,282,486,468,190,283,487,469,225,191,484,280,466,229,192,485,281,467,230,193,483,279,465,228,194,680,677,679,678,290,489,512,517,525,288,510,518,526,490,289,491,511,516,527,508,286,492,513,528,287,509,493,514,529,285,507,494,515,530,296,503,495,523,531,524,294,501,496,532,295,502,497,522,533,506,292,498,519,534,504,293,499,520,535,505,291,500,521,536,689,690,691,692,299,23,162,177,591,297,160,175,592,21,298,22,161,176,593,165,302,19,173,594,300,163,20,174,595,301,164,18,172,596,305,157,14,168,589,166,303,158,12,590,304,159,13,167,588,156,308,17,171,585,154,306,15,169,586,155,307,16,170,587,697,698,700,699,107,640,655,27,92,105,653,28,90,638,106,639,654,29,91,651,103,643,26,95,104,652,641,24,93,102,650,642,25,94,98,646,635,33,87,34,96,644,636,88,97,645,637,35,89,649,101,634,32,86,647,99,632,30,84,648,100,633,31,85,661,662,664,663,143,381,403,365,379,144,404,363,380,382,142,383,402,364,378,399,146,384,368,375,147,400,385,366,376,145,401,386,367,377,149,394,387,360,370,361,150,395,388,371,148,393,389,362,369,397,152,390,359,373,398,153,391,357,374,396,151,392,358,372,682,681,684,683,36,113,603,312,188,37,604,313,186,114,38,112,602,314,187,606,39,116,311,184,40,607,117,309,185,41,605,115,310,183,42,601,320,318,179,319,43,600,108,178,44,658,657,656,659,598,45,110,317,182,599,46,111,315,180,597,47,109,316,181,693,694,696,695,7,575,537,559,562,8,538,560,563,573,6,574,539,558,561,540,10,578,555,565,11,541,576,556,566,9,542,577,557,564,5,543,581,550,568,551,3,544,579,569,4,545,580,549,567,546,0,584,553,571,547,2,582,554,572,548,1,583,552,570,666,665,668,667,258,433,442,410,422,259,443,408,420,434,260,432,441,409,421,445,257,429,406,418,255,446,430,407,419,256,444,431,405,417,249,448,439,416,428,414,250,449,440,426,251,447,438,415,427,451,252,435,412,424,452,253,436,413,425,450,254,437,411,423,674,673,676,675 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#cd941b7de786c28317b7a103413c14ee77b5f1d3c398e3760811607e92439ad2, 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 20:43:19 · history