Equation 677 Database

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Magma da871ac07eaa…

magma da871ac07eaa
Size
705
Isomorphism class hash
da871ac07eaa80035af63ab7b25bdfb70eea1ea41015b17b4a359f5bf3b74ae9
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 15:23:50
Display reorder
704,41,40,42,43,44,45,46,47,33,34,35,36,37,38,39,61,62,48,49,50,51,52,53,54,55,56,57,58,59,60,32,18,19,20,21,22,23,24,25,26,27,28,29,30,15,16,17,3,4,5,6,7,8,9,10,11,12,13,14,31,682,683,680,681,616,615,617,603,604,605,606,607,608,609,610,611,612,613,614,621,622,623,624,625,626,627,628,629,630,631,632,618,619,620,650,651,652,653,654,655,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,2,1,0,658,659,657,656,703,702,701,700,568,567,569,570,571,572,558,559,560,561,562,563,564,565,566,554,555,556,557,543,544,545,546,547,548,549,550,551,552,553,591,592,593,594,595,596,597,598,599,600,601,602,588,589,586,587,573,574,575,576,577,578,579,580,581,582,583,584,585,590,670,671,668,669,436,435,437,423,424,425,426,427,428,429,430,431,432,433,434,441,442,443,444,445,446,447,448,449,450,451,452,438,439,440,462,463,464,465,466,467,453,454,455,456,457,458,459,460,470,471,472,473,474,475,476,477,478,479,480,481,482,468,469,461,679,677,678,676,142,141,143,144,145,146,147,148,149,150,151,152,138,139,140,125,126,127,128,129,130,131,132,133,134,135,136,137,123,124,174,175,176,177,178,179,180,181,182,168,169,170,171,172,163,164,165,166,167,153,154,155,156,157,158,159,160,161,162,173,691,690,688,689,260,259,261,262,263,264,265,266,267,268,269,270,271,272,258,252,253,254,255,256,257,243,244,245,246,247,248,249,250,251,295,296,297,298,299,300,301,302,288,289,290,291,292,293,287,273,274,275,276,277,278,279,280,281,282,283,284,285,286,294,695,694,693,692,111,110,112,113,114,115,116,117,118,119,120,121,122,108,109,106,107,93,94,95,96,97,98,99,100,101,102,103,104,105,77,63,64,65,66,67,68,69,70,71,72,73,74,75,85,86,87,88,89,90,91,92,78,79,80,81,82,83,84,76,663,662,661,660,332,331,318,319,320,321,322,323,324,325,326,327,328,329,330,315,316,317,303,304,305,306,307,308,309,310,311,312,313,314,349,350,351,352,353,354,355,356,357,358,359,360,361,362,338,339,340,341,342,343,344,345,346,347,333,334,335,336,337,348,686,687,685,684,379,378,380,381,382,383,384,385,386,387,388,389,390,391,392,368,369,370,371,372,373,374,375,376,377,363,364,365,366,367,408,409,410,411,412,413,414,415,416,417,418,419,420,421,394,395,396,397,398,399,400,401,402,403,404,405,406,407,393,422,696,697,699,698,529,528,530,531,532,533,534,535,536,537,538,539,540,541,542,518,519,520,521,522,523,524,525,526,527,513,514,515,516,517,483,484,485,486,487,488,489,490,491,492,493,494,495,496,509,510,511,512,498,499,500,501,502,503,504,505,506,507,508,497,664,665,667,666,212,211,198,199,200,201,202,203,204,205,206,207,208,209,210,195,196,197,183,184,185,186,187,188,189,190,191,192,193,194,229,230,231,232,233,234,235,236,237,238,239,240,241,242,218,219,220,221,222,223,224,225,226,227,213,214,215,216,217,228,675,674,673,672 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#17d8eb76b6bf5b6d0c7c94cbffab8bf30c3f61585a1079f6e7ebccc76f8bf7d1, 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 15:23:51 · history