Equation 677 Database

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Magma 31d434438f04…

magma 31d434438f04
Size
705
Isomorphism class hash
31d434438f041eb2c8d403a30d44eea397799773d26957b0e0fc004c883f7264
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 18:08:40
Display reorder
660,351,621,144,358,22,145,622,356,23,352,620,350,146,357,21,354,147,624,361,18,148,355,625,359,19,149,353,623,360,20,627,349,364,150,13,628,347,362,151,14,626,348,363,152,12,345,630,367,153,16,346,631,365,154,17,155,344,629,366,15,687,688,686,685,455,9,434,475,450,435,10,473,451,456,11,457,436,474,449,454,437,8,471,446,438,452,6,472,447,439,453,7,470,448,1,461,466,432,441,0,462,464,433,442,2,463,465,431,440,460,3,469,428,444,458,4,467,429,445,430,459,5,468,443,703,704,701,702,615,135,329,311,332,330,136,312,333,616,137,614,331,313,334,618,328,134,310,335,326,619,132,308,336,327,617,133,309,337,141,613,317,320,338,142,611,318,321,339,143,612,319,322,340,609,140,316,323,341,610,138,314,324,342,325,608,139,315,343,671,672,670,669,261,478,241,223,244,242,476,224,245,259,477,260,243,225,246,257,240,481,222,247,238,258,479,220,248,239,256,480,221,249,484,267,229,232,250,482,265,230,233,251,483,266,231,234,252,263,487,228,235,253,264,485,226,236,254,237,262,486,227,255,679,680,678,677,505,114,527,517,493,528,115,515,491,503,116,504,529,516,492,501,526,117,513,489,524,502,118,514,490,525,500,119,512,488,112,511,523,533,499,113,509,521,534,497,111,510,522,535,498,507,108,519,532,495,508,109,520,530,496,531,506,110,518,494,692,691,690,689,126,38,592,199,288,590,36,200,286,127,37,128,591,198,287,129,595,41,202,291,593,130,39,203,289,594,131,40,201,290,44,124,197,587,283,42,125,195,588,284,43,123,196,589,285,120,47,193,586,282,121,45,194,584,280,585,122,46,192,281,699,700,698,697,70,54,93,75,96,94,55,76,97,71,56,69,95,77,98,66,92,57,74,99,90,67,58,72,100,91,68,59,73,101,52,61,81,84,102,53,62,82,85,103,51,60,83,86,104,64,48,80,87,105,65,49,78,88,106,89,63,50,79,107,663,664,662,661,29,634,158,374,169,156,632,375,170,27,633,28,157,376,168,25,161,637,377,172,159,26,635,378,173,160,24,636,379,171,640,35,372,164,175,638,33,373,162,176,639,34,371,163,174,31,643,368,167,178,32,641,369,165,179,166,30,642,370,177,682,683,684,681,657,604,658,656,659,650,602,648,651,649,603,653,654,652,655,211,299,607,219,301,646,645,605,644,647,298,210,606,218,300,599,206,214,297,305,600,204,212,295,306,601,205,213,296,307,209,598,217,293,304,207,596,215,294,302,292,208,597,216,303,695,696,693,694,577,272,553,541,565,551,273,539,563,575,271,576,552,540,564,573,549,268,537,561,550,574,269,538,562,548,572,270,536,560,278,583,547,559,571,279,581,545,557,569,277,582,546,558,570,579,274,543,555,567,580,275,544,556,568,554,578,276,542,566,667,668,665,666,402,181,427,407,386,425,182,408,387,403,180,401,426,409,388,398,423,184,406,389,424,399,185,404,390,422,400,183,405,391,187,393,413,418,384,188,394,414,416,385,186,392,415,417,383,396,190,412,421,380,397,191,410,419,381,420,395,189,411,382,675,676,673,674 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#65ec2d14586b016399098bfd783683584e63e97f4655962a7b7e32e1fef46a76, 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 18:08:41 · history