Equation 677 Database

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Magma 30af912040ce…

magma 30af912040ce
Size
705
Isomorphism class hash
30af912040cece0691b995e9d196f7242372f21da4448ff5bd91acfd23746008
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 15:52:26
Display reorder
661,246,248,247,251,249,250,243,244,245,242,240,241,94,95,93,90,91,92,85,86,84,88,89,87,69,70,71,68,66,67,60,61,62,63,64,65,575,573,574,571,572,570,566,564,565,569,567,568,435,436,437,434,432,433,441,442,443,440,438,439,679,685,682,688,26,25,24,28,29,27,31,32,30,34,35,33,149,147,148,145,146,144,155,153,154,151,152,150,473,471,472,469,470,468,479,477,478,475,476,474,49,50,48,52,53,51,55,56,54,58,59,57,615,616,617,614,612,613,621,622,623,620,618,619,691,696,703,702,165,167,166,163,164,162,158,156,157,161,159,160,430,431,429,426,427,428,421,422,420,424,425,423,239,237,238,235,236,234,230,228,229,233,231,232,561,562,563,560,558,559,552,553,554,555,556,557,76,77,75,72,73,74,82,83,81,78,79,80,665,673,668,675,503,502,501,498,499,500,493,494,492,496,497,495,632,630,631,635,633,634,627,628,629,626,624,625,490,491,489,486,487,488,481,482,480,484,485,483,370,371,369,366,367,368,361,362,360,364,365,363,1,0,2,3,4,5,6,7,8,9,10,11,677,683,681,687,332,331,330,334,335,333,329,327,328,325,326,324,21,22,23,20,18,19,12,13,14,15,16,17,644,642,643,647,645,646,639,640,641,638,636,637,504,505,506,507,508,509,510,511,512,513,514,515,374,372,373,377,375,376,380,378,379,383,381,382,689,698,693,700,184,183,185,182,180,181,189,190,191,188,186,187,320,318,319,323,321,322,315,316,317,314,312,313,354,355,356,357,358,359,352,353,351,348,349,350,396,397,398,399,400,401,402,403,404,405,406,407,536,534,535,539,537,538,531,532,533,530,528,529,692,695,694,704,277,276,278,279,280,281,282,283,284,285,286,287,289,290,288,292,293,291,295,296,294,298,299,297,302,300,301,305,303,304,308,306,307,311,309,310,275,273,274,271,272,270,266,264,265,269,267,268,178,179,177,174,175,176,169,170,168,172,173,171,660,662,667,663,449,448,447,444,445,446,454,455,453,450,451,452,258,259,260,261,262,263,256,257,255,252,253,254,596,594,595,599,597,598,591,592,593,590,588,589,107,105,106,103,104,102,98,96,97,101,99,100,587,585,586,583,584,582,578,576,577,581,579,580,678,684,680,686,548,547,546,550,551,549,545,543,544,541,542,540,412,413,411,408,409,410,418,419,417,414,415,416,208,209,207,204,205,206,214,215,213,210,211,212,221,219,220,217,218,216,227,225,226,223,224,222,192,193,194,195,196,197,198,199,200,201,202,203,690,699,697,701,389,388,387,384,385,386,394,395,393,390,391,392,337,338,336,340,341,339,343,344,342,346,347,345,43,44,42,46,47,45,41,39,40,37,38,36,524,522,523,527,525,526,519,520,521,518,516,517,653,651,652,649,650,648,659,657,658,655,656,654,664,672,670,676,460,459,461,458,456,457,465,466,467,464,462,463,610,611,609,606,607,608,601,602,600,604,605,603,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,134,132,133,137,135,136,140,138,139,143,141,142,666,671,669,674 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {63} 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 15:52:27 · history