Equation 677 Database

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Magma 33e632f7fc39…

magma 33e632f7fc39
Size
705
Isomorphism class hash
33e632f7fc39eb1df9c03eb87295ce5e55531c2edf4b5997cb85156e34af1a0c
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 18:20:58
Display reorder
660,49,396,387,301,291,50,397,388,302,292,51,398,389,300,293,395,52,390,297,294,53,393,391,298,295,394,54,392,299,296,385,47,402,307,289,386,48,403,308,290,384,46,404,306,288,43,381,401,303,285,44,382,399,304,286,45,383,400,305,287,685,686,688,687,169,379,61,448,32,170,380,62,449,33,168,378,63,447,35,375,172,64,451,37,173,376,65,452,40,377,171,66,450,42,59,167,370,446,34,60,165,371,444,36,58,166,369,445,31,163,55,373,442,39,164,56,374,443,41,162,57,372,441,38,701,702,704,703,589,283,607,581,568,587,284,605,582,566,588,282,606,583,567,279,585,603,580,571,586,280,604,578,569,281,584,602,579,570,598,595,274,572,563,596,593,275,573,564,597,594,273,574,565,591,601,277,575,562,592,599,278,576,560,590,600,276,577,561,670,669,672,671,474,184,481,463,491,475,185,482,464,489,476,183,480,462,490,180,473,477,459,494,471,181,478,460,492,182,472,479,461,493,487,465,175,454,497,488,466,176,455,495,486,467,174,453,496,468,483,178,457,500,469,484,179,458,498,470,485,177,456,499,680,677,679,678,156,195,508,90,513,157,196,509,91,514,158,197,507,92,515,194,159,511,93,516,160,192,512,94,517,193,161,510,95,518,506,154,186,96,519,504,155,187,97,520,505,153,188,98,521,150,502,189,99,522,151,503,190,100,523,152,501,191,101,524,689,690,691,692,87,247,109,145,545,88,248,110,146,543,89,246,108,144,544,250,86,112,148,548,84,251,113,149,546,249,85,111,147,547,107,78,253,143,540,105,79,254,141,541,106,80,252,142,542,81,103,256,139,539,82,104,257,140,537,83,102,255,138,538,697,698,700,699,637,27,655,629,616,635,25,653,630,614,636,26,654,631,615,30,633,651,628,619,634,28,652,626,617,29,632,650,627,618,646,643,22,620,611,644,641,23,621,612,645,642,24,622,613,639,649,21,623,610,640,647,19,624,608,638,648,20,625,609,661,662,664,663,332,121,412,317,419,330,122,413,315,417,331,120,411,316,418,124,328,415,320,422,329,125,416,318,420,123,327,414,319,421,410,323,119,312,425,408,321,117,313,423,409,322,118,314,424,326,406,115,311,428,324,407,116,309,426,325,405,114,310,427,682,681,684,683,261,14,3,556,69,262,15,0,554,67,263,13,2,555,68,17,260,6,559,72,258,18,4,557,70,16,259,5,558,71,269,267,12,552,77,1,268,10,553,73,657,656,11,658,659,266,272,8,551,76,264,270,9,549,74,265,271,7,550,75,693,694,696,695,226,527,234,221,208,227,525,235,219,209,225,526,236,220,207,530,222,237,217,204,223,528,238,218,205,529,224,239,216,206,240,232,533,212,199,241,233,531,210,200,242,231,532,211,198,228,243,536,215,202,229,244,534,213,203,230,245,535,214,201,666,665,668,667,350,435,368,339,127,348,436,366,340,128,349,437,367,341,126,438,346,364,342,130,347,439,365,343,131,440,345,363,344,129,359,356,433,337,133,357,354,434,338,134,358,355,432,336,132,352,362,429,333,136,353,360,430,334,137,351,361,431,335,135,674,673,676,675 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#7bddf6e5b82b5432712e2579d3d5db84306ca98ed650c79ff87e357573a5998e, 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 18:20:59 · history