Equation 677 Database

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Magma eadedd0b96e0…

magma eadedd0b96e0
Size
705
Isomorphism class hash
eadedd0b96e004b0431040757f8beb090fa587bc4d1476043aff12732b347669
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 19:50:04
Display reorder
660,331,336,355,435,360,356,332,436,361,337,354,338,330,437,362,335,351,327,434,359,333,352,328,432,357,334,353,329,433,358,342,346,441,322,366,343,347,442,323,367,344,345,443,321,368,349,341,440,325,365,350,339,438,326,363,348,340,439,324,364,685,686,688,687,488,161,143,228,3,141,486,229,4,159,142,160,487,230,5,157,139,491,231,2,158,140,489,232,1,156,138,490,233,0,167,134,234,483,9,165,132,235,484,10,166,133,236,485,11,137,163,237,482,8,135,164,238,480,6,136,162,239,481,7,701,702,704,703,107,416,431,623,313,429,105,621,314,414,430,415,106,622,312,419,427,103,619,309,417,428,104,620,310,418,426,102,618,311,411,422,614,98,319,412,420,612,96,320,413,421,613,97,318,425,410,617,101,315,423,408,615,99,316,424,409,616,100,317,670,669,672,671,262,269,179,499,248,177,263,500,246,267,178,268,261,498,247,265,175,258,502,251,266,176,259,503,249,264,174,260,501,250,275,170,497,253,243,273,168,495,254,244,274,169,496,252,245,173,271,493,256,242,171,272,494,257,240,172,270,492,255,241,680,677,679,678,519,539,21,120,511,22,520,121,512,537,23,538,521,122,510,535,20,518,123,514,536,18,516,124,515,534,19,517,125,513,530,12,126,525,509,528,13,127,526,507,529,14,128,527,508,15,533,129,524,505,16,531,130,522,506,17,532,131,523,504,689,690,691,692,585,593,562,296,567,563,586,294,568,591,561,592,587,295,569,589,558,584,299,566,590,559,582,297,564,588,560,583,298,565,599,553,291,576,573,597,554,292,577,574,598,552,293,578,575,556,595,290,579,572,557,596,288,580,570,555,594,289,581,571,697,698,700,699,69,632,647,76,114,645,70,77,115,630,646,631,71,75,116,635,643,68,72,117,633,644,66,73,118,634,642,67,74,119,627,638,82,60,112,628,636,83,61,113,629,637,81,62,111,641,626,78,63,108,639,624,79,64,109,640,625,80,65,110,661,662,664,663,201,451,461,375,188,459,202,376,186,452,460,450,203,377,187,454,457,200,378,191,455,458,198,379,189,453,456,199,380,190,449,467,373,192,183,447,465,374,193,184,448,466,372,194,185,463,445,369,195,182,464,446,370,196,180,462,444,371,197,181,682,681,684,683,388,395,399,606,306,400,389,607,307,393,401,394,387,608,308,391,402,384,609,305,392,403,385,610,303,390,404,386,611,304,654,655,604,652,653,656,659,605,658,657,649,650,603,648,651,405,397,600,382,300,406,398,601,383,301,407,396,602,381,302,693,694,696,695,92,35,37,280,546,38,90,281,547,33,36,34,91,279,548,31,40,95,276,549,32,41,93,277,550,30,39,94,278,551,26,43,286,87,544,24,44,287,88,545,25,42,285,89,543,46,29,282,86,540,47,27,283,84,541,45,28,284,85,542,666,665,668,667,152,474,215,59,216,213,150,57,217,475,214,476,151,58,218,477,211,155,55,219,478,212,153,56,220,479,210,154,54,221,472,206,50,147,222,473,204,48,148,223,471,205,49,149,224,209,468,53,146,225,207,469,51,144,226,208,470,52,145,227,674,673,676,675 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#b0c577ef9e4c05d7925e972279aa7c10376825c460b06aa55c85bf856c0bbca9, 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 19:50:05 · history