Equation 677 Database

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Magma 34c98c3dd030…

magma 34c98c3dd030
Size
705
Isomorphism class hash
34c98c3dd03073a2c9a1c2685d1c23564e669382fb3180cf42993bfbd2387134
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 19:10:13
Display reorder
660,51,59,349,342,614,52,612,57,350,343,58,613,53,348,344,62,54,617,352,345,60,55,615,353,346,616,56,61,351,347,355,65,49,620,340,63,50,618,356,341,64,48,619,354,339,45,68,623,358,336,46,66,621,359,337,47,67,622,357,338,687,688,686,685,230,446,438,242,207,228,208,444,439,240,445,209,229,440,241,449,226,210,441,238,447,227,211,442,239,212,225,448,443,237,436,452,221,213,233,450,219,214,437,231,451,220,215,435,232,224,455,216,432,236,222,453,217,433,234,223,454,218,434,235,703,704,701,702,80,602,594,35,324,78,325,600,595,33,601,326,79,596,34,605,76,327,597,38,603,77,328,598,36,329,75,604,599,37,592,608,71,330,41,606,69,331,593,39,607,70,332,591,40,74,611,333,588,44,72,609,334,589,42,73,610,335,590,43,671,672,670,669,264,243,290,271,464,265,462,244,288,272,245,463,266,289,270,246,263,467,286,267,247,261,465,287,268,466,262,248,285,269,281,249,255,459,277,250,256,460,279,278,251,257,461,280,276,258,252,458,284,273,259,253,456,282,274,260,254,457,283,275,679,680,678,677,501,480,474,507,147,502,148,481,475,508,482,149,503,476,509,483,500,150,477,506,484,498,151,478,504,152,499,485,479,505,472,486,492,145,513,487,493,146,473,514,488,494,144,471,515,495,489,141,468,512,496,490,142,469,510,497,491,143,470,511,692,691,690,689,572,168,160,309,22,570,23,169,161,310,170,21,571,159,311,167,575,18,163,312,165,573,19,164,313,20,574,166,162,314,158,174,567,13,307,175,568,14,156,308,176,569,12,157,306,566,173,16,154,303,564,171,17,155,304,565,172,15,153,305,699,700,698,697,119,107,98,129,88,117,89,105,96,130,106,87,118,97,131,110,122,91,94,132,108,120,92,95,133,90,121,109,93,134,104,113,125,86,135,111,123,84,102,136,112,124,85,103,137,128,116,82,100,138,126,114,83,101,139,127,115,81,99,140,663,664,662,661,360,638,630,381,5,361,3,636,631,382,637,4,362,632,383,641,363,0,633,380,639,364,2,634,378,1,365,640,635,379,628,644,366,11,372,642,367,9,629,373,643,368,10,627,374,369,647,7,624,375,370,645,8,625,376,371,646,6,626,377,682,683,684,681,183,25,321,186,583,184,584,26,322,187,24,582,185,323,188,657,656,586,659,658,648,649,587,650,651,585,653,652,655,654,319,31,181,581,192,32,182,579,320,193,30,180,580,318,194,177,27,577,315,191,178,28,578,316,189,179,29,576,317,190,695,696,693,694,526,557,550,532,293,527,291,555,551,533,556,292,525,549,531,553,522,296,546,528,554,523,294,547,529,295,524,552,548,530,541,563,517,299,538,561,518,297,542,539,562,516,298,540,537,520,559,302,544,534,521,560,300,545,535,519,558,301,543,536,667,668,665,666,413,405,395,422,205,411,206,406,393,420,407,204,412,394,421,404,409,201,391,425,402,410,202,392,423,203,408,403,390,424,386,396,419,196,428,397,417,197,384,426,398,418,195,385,427,415,399,199,389,431,416,400,200,387,429,414,401,198,388,430,675,676,673,674 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#8e5759f62ba231b7a190308c910bac46805bb85b5237b53b53611999ba1c2d7b, 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 19:10:14 · history