Equation 677 Database

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Magma 2271ace97d96…

magma 2271ace97d96
Size
705
Isomorphism class hash
2271ace97d9687aa745f0f64317d5f0b16804f2776e0c4c3ba58f2f9332b8c08
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 21:46:35
Display reorder
660,245,266,351,258,357,243,264,352,259,358,244,265,353,260,359,262,248,354,257,360,263,355,255,361,246,261,247,356,256,362,240,349,272,249,363,241,350,270,250,364,242,348,271,251,365,345,239,268,252,366,253,346,237,269,367,347,238,267,254,368,685,686,688,687,142,421,432,409,402,140,422,433,410,403,141,420,434,408,404,417,145,431,405,401,418,429,406,399,143,419,144,430,407,400,148,438,427,415,393,146,439,428,416,394,147,440,426,414,395,437,151,423,411,396,412,435,149,424,397,436,150,425,413,398,701,702,704,703,235,543,555,577,567,236,541,553,578,565,234,542,554,579,566,539,231,551,576,563,540,552,574,564,232,538,233,550,575,562,226,546,534,568,558,227,544,532,569,556,225,545,533,570,557,549,229,537,571,561,572,547,230,535,559,548,228,536,573,560,670,669,672,671,442,158,94,123,100,443,159,95,124,101,441,160,96,122,102,161,445,93,126,99,162,91,127,97,446,163,444,92,125,98,448,85,156,121,106,449,86,157,119,107,447,87,155,120,108,88,451,152,117,105,118,89,452,153,103,90,450,154,116,104,680,677,679,678,166,84,72,460,46,164,82,70,461,47,165,83,71,459,48,80,169,68,463,45,81,69,464,43,167,79,168,67,462,44,172,63,75,458,37,170,61,73,456,38,171,62,74,457,39,66,175,78,454,40,455,64,173,76,41,65,174,77,453,42,689,690,691,692,333,201,60,194,521,334,202,58,195,519,335,200,59,196,520,204,336,56,197,524,205,57,198,522,337,203,338,55,199,523,339,51,207,192,516,340,49,208,193,517,341,50,206,191,518,54,342,210,188,515,189,52,343,211,513,53,344,209,190,514,697,698,700,699,590,627,639,615,603,591,625,637,613,601,589,626,638,614,602,623,586,635,611,599,624,636,612,600,587,622,588,634,610,598,581,630,618,606,594,582,628,616,604,592,580,629,617,605,593,633,584,621,609,597,607,631,585,619,595,632,583,620,608,596,661,662,664,663,380,284,296,318,308,378,282,294,319,306,379,283,295,320,307,280,376,292,317,304,281,293,315,305,377,279,375,291,316,303,371,287,275,309,299,369,285,273,310,297,370,286,274,311,298,290,374,278,312,302,313,288,372,276,300,289,373,277,314,301,682,681,684,683,11,221,215,526,112,12,219,216,527,113,10,220,217,528,114,224,7,214,529,111,222,212,530,109,8,223,9,213,531,110,2,646,644,647,645,3,218,1,525,115,0,640,641,642,643,658,5,657,659,656,651,650,6,649,648,654,4,653,655,652,693,694,696,695,178,503,471,494,477,176,501,472,492,478,177,502,473,493,479,506,181,474,490,480,504,475,491,481,179,505,180,476,489,482,184,469,509,500,483,182,470,507,498,484,183,468,508,499,485,465,187,512,496,486,497,466,185,510,487,467,186,511,495,488,666,665,668,667,136,332,32,388,22,134,330,33,389,20,135,331,34,387,21,328,139,31,391,18,329,29,392,19,137,327,138,30,390,17,131,23,323,386,13,132,24,321,384,14,133,25,322,385,15,26,130,326,382,16,383,27,128,324,36,28,129,325,381,35,674,673,676,675 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#f4f724834d898f30c0a6fbb58eb0b496232f556dc00d71550d6e526db5e670b8, 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 21:46:36 · history